Yes, I know that not all the stars in the Hipparcos catalogue has a name.
I have found that, the following catalogue has some stars' names:
(HR) Bright Star Catalogue, 5th Revised Ed. (Hoffleit+, 1991) (V/50)
But, do you know where I can find the Greek letters of the stars?
Maybe, there is a catalogue in which I can use the HIP number to get the star's Greek letter.
The HIPPARCOS catalog has two files named ident4.doc and ident6.doc which contain common names and Flamsteed designations. The files are available via CDS:
https://cdsarc.cds.unistra.fr/ftp/I/239/version_cd/tables/
An extracted version of the common named file mapped to the most important fields: https://www.celestialprogramming.com/snippets/CommonStarNames.html
Header , HIP ID , RA , Dec , Mag , Parallax , Pm RA , Pm Dec
Acamar , 13847 , 44.56531119 , -40.30467242 , 2.88 , 20.22 , -53.53 , 25.71
Achernar , 7588 , 24.42852736 , -57.23675749 , 0.45 , 22.68 , 88.02 , -40.08
Acrux , 60718 , 186.64956584 , -63.09909166 , 0.77 , 10.17 , -35.37 , -14.73
Adhara , 33579 , 104.65645182 , -28.97208374 , 1.50 , 7.57 , 2.63 , 2.29
Agena , 68702 , 210.95585201 , -60.37303931 , 0.61 , 6.21 , -33.96 , -25.06
Albireo , 95947 , 292.68033578 , 27.95968112 , 3.05 , 8.46 , -7.09 , -5.63
Alcor , 65477 , 201.30640816 , 54.98795767 , 3.99 , 40.19 , 120.35 , -16.94
Alcyone , 17702 , 56.87115217 , 24.10513715 , 2.85 , 8.87 , 19.35 , -43.11
Aldebaran , 21421 , 68.98016110 , 16.50930139 , 0.87 , 50.09 , 62.78 , -189.36
Alderamin , 105199 , 319.64488119 , 62.58557261 , 2.45 , 66.84 , 149.91 , 48.27
Algenib , 1067 , 3.30897012 , 15.18359590 , 2.83 , 9.79 , 4.70 , -8.24
Algieba , 50583 , 154.99314355 , 19.84148873 , 2.01 , 25.96 , 310.77 , -152.88
Algol , 14576 , 47.04221485 , 40.95564770 , 2.09 , 35.14 , 2.39 , -1.44
Alhena , 31681 , 99.42792124 , 16.39925217 , 1.93 , 31.12 , -2.04 , -66.92
Alioth , 62956 , 193.50728928 , 55.95982116 , 1.76 , 40.30 , 111.74 , -8.99
Alkaid , 67301 , 206.88515682 , 49.31326506 , 1.85 , 32.39 , -121.23 , -15.56
Almaak , 9640 , 30.97480447 , 42.32972473 , 2.10 , 9.19 , 43.08 , -50.85
Alnair , 109268 , 332.05827280 , -46.96097543 , 1.73 , 32.16 , 127.60 , -147.91
Alnath , 25428 , 81.57297249 , 28.60745001 , 1.65 , 24.89 , 23.28 , -174.22
Alnilam , 26311 , 84.05338934 , -1.20191983 , 1.69 , 2.43 , 1.49 , -1.06
Alnitak , 26727 , 85.18969642 , -1.94257224 , 1.74 , 3.99 , 3.99 , 2.54
Alphard , 46390 , 141.89684698 , -8.65860253 , 1.99 , 18.40 , -14.49 , 33.25
Alphekka , 76267 , 233.67195048 , 26.71469302 , 2.22 , 43.65 , 120.38 , -89.44
Alpheratz , 677 , 2.09691071 , 29.09043199 , 2.07 , 33.60 , 135.68 , -162.95
Alshain , 98036 , 298.82830569 , 6.40676346 , 3.71 , 72.95 , 46.35 , -481.32
Altair , 97649 , 297.69582916 , 8.86832198 , 0.76 , 194.44 , 536.82 , 385.54
Ankaa , 2081 , 6.57104571 , -42.30598151 , 2.40 , 42.14 , 232.76 , -353.64
Antares , 80763 , 247.35192046 , -26.43200249 , 1.06 , 5.40 , -10.16 , -23.21
Arcturus , 69673 , 213.91530010 , 19.18241030 , -0.05 , 88.85 , -1093.45 , -1999.40
Arneb , 25985 , 83.18256633 , -17.82228853 , 2.58 , 2.54 , 3.27 , 1.54
Babcock's star , 112247 , 341.03127284 , 55.58922579 , 8.83 , 1.40 , 4.96 , -0.98
Barnard's star , 87937 , 269.45207733 , 4.69338832 , 9.54 , 549.01 , -797.84 , 10326.93
Bellatrix , 25336 , 81.28276276 , 6.34970223 , 1.64 , 13.42 , -8.75 , -13.28
Betelgeuse , 27989 , 88.79293860 , 7.40706274 , 0.45 , 7.63 , 27.33 , 10.86
Campbell's star , 96295 , 293.68846814 , 30.51637117 , 10.00 , -1.63 , -4.16 , -10.19
Canopus , 30438 , 95.98795780 , -52.69566046 , -0.62 , 10.43 , 19.99 , 23.67
Capella , 24608 , 79.17232940 , 45.99799111 , 0.08 , 77.29 , 75.52 , -427.13
Caph , 746 , 2.29452113 , 59.14977960 , 2.28 , 59.89 , 523.39 , -180.42
Castor , 36850 , 113.64942834 , 31.88827629 , 1.58 , 63.27 , -206.33 , -148.18
Cor Caroli , 63125 , 194.00694736 , 38.31837980 , 2.89 , 29.60 , -233.43 , 54.98
Cyg X-1 , 98298 , 299.59031505 , 35.20160419 , 8.84 , 0.58 , -3.82 , -7.62
Deneb , 102098 , 310.35797809 , 45.28033800 , 1.25 , 1.01 , 1.56 , 1.55
Denebola , 57632 , 177.26490656 , 14.57206032 , 2.14 , 90.16 , -499.02 , -113.78
Diphda , 3419 , 10.89737940 , -17.98660460 , 2.04 , 34.04 , 232.79 , 32.71
Dubhe , 54061 , 165.93195289 , 61.75103320 , 1.81 , 26.38 , -136.46 , -35.25
Enif , 107315 , 326.04649214 , 9.87501126 , 2.38 , 4.85 , 30.02 , 1.38
Etamin , 87833 , 269.15154113 , 51.48889499 , 2.24 , 22.10 , -8.52 , -23.05
Fomalhaut , 113368 , 344.41269372 , -29.62223615 , 1.17 , 130.08 , 329.22 , -164.22
Groombridge 1830 , 57939 , 178.24487003 , 37.71867881 , 6.42 , 109.21 , 4003.69 , -5813.00
Hadar , 68702 , 210.95585201 , -60.37303931 , 0.61 , 6.21 , -33.96 , -25.06
Hamal , 9884 , 31.79336293 , 23.46242313 , 2.01 , 49.48 , 190.73 , -145.77
Izar , 72105 , 221.24674043 , 27.07422244 , 2.35 , 15.55 , -50.65 , 20.00
Kapteyn's star , 24186 , 77.91909105 , -45.01841505 , 8.86 , 255.26 , 6506.05 , -5731.39
Kaus Australis , 90185 , 276.04299301 , -34.38461611 , 1.79 , 22.55 , -39.61 , -124.05
Kocab , 72607 , 222.67636006 , 74.15550491 , 2.07 , 25.79 , -32.29 , 11.91
Kruger 60 , 110893 , 336.99778215 , 57.69587495 , 9.59 , 249.52 , -870.23 , -471.10
Luyten's star , 36208 , 111.85207979 , 5.22578524 , 9.84 , 263.26 , 571.27 , -3694.25
Markab , 113963 , 346.19022409 , 15.20526442 , 2.49 , 23.36 , 61.10 , -42.56
Megrez , 59774 , 183.85650051 , 57.03261690 , 3.32 , 40.05 , 103.56 , 7.81
Menkar , 14135 , 45.56988401 , 4.08973396 , 2.54 , 14.82 , -11.81 , -78.76
Merak , 53910 , 165.46031999 , 56.38242679 , 2.34 , 41.07 , 81.66 , 33.74
Mintaka , 25930 , 83.00166968 , -0.29909204 , 2.25 , 3.56 , 1.67 , 0.56
Mira , 10826 , 34.83663617 , -2.97764262 , 6.47 , 7.79 , 10.33 , -239.48
Mirach , 5447 , 17.43301493 , 35.62055770 , 2.07 , 16.36 , 175.59 , -112.23
Mirphak , 15863 , 51.08070979 , 49.86117959 , 1.79 , 5.51 , 24.11 , -26.01
Mizar , 65378 , 200.98142880 , 54.92536175 , 2.23 , 41.73 , 121.23 , -22.01
Nihal , 25606 , 82.06134664 , -20.75944097 , 2.81 , 20.49 , -5.03 , -85.92
Nunki , 92855 , 283.81635716 , -26.29672225 , 2.05 , 14.54 , 13.87 , -52.65
Phad , 58001 , 178.45769772 , 53.69476008 , 2.41 , 38.99 , 107.76 , 11.16
Pleione , 17851 , 57.29673351 , 24.13671205 , 5.05 , 8.42 , 18.71 , -46.74
Polaris , 11767 , 37.95451535 , 89.26410951 , 1.97 , 7.56 , 44.22 , -11.74
Pollux , 37826 , 116.32895983 , 28.02619862 , 1.16 , 96.74 , -625.69 , -45.95
Procyon , 37279 , 114.82549301 , 5.22499306 , 0.40 , 285.93 , -716.57 , -1034.58
Proxima , 70890 , 217.42895285 , -62.67948359 , 11.01 , 772.33 , -3775.64 , 768.16
Rasalgethi , 84345 , 258.66191003 , 14.39033281 , 2.78 , 8.53 , -6.71 , 32.78
Rasalhague , 86032 , 263.73362733 , 12.56003477 , 2.08 , 69.84 , 110.08 , -222.61
Red Rectangle , 30089 , 94.99256656 , -10.63741419 , 8.85 , 2.62 , -10.98 , -21.10
Regulus , 49669 , 152.09296110 , 11.96720706 , 1.36 , 42.09 , -249.40 , 4.91
Rigel , 24436 , 78.63446812 , -8.20164055 , 0.18 , 4.22 , 1.87 , -0.56
Rigil Kent , 71683 , 219.90206584 , -60.83397468 , -0.01 , 742.12 , -3678.19 , 481.84
Sadalmelik , 109074 , 331.44598220 , -0.31985070 , 2.95 , 4.30 , 17.90 , -9.93
Saiph , 27366 , 86.93912023 , -9.66960478 , 2.07 , 4.52 , 1.55 , -1.20
Scheat , 113881 , 345.94357301 , 28.08278909 , 2.44 , 16.37 , 187.76 , 137.61
Shaula , 85927 , 263.40216661 , -37.10382115 , 1.62 , 4.64 , -8.90 , -29.95
Shedir , 3179 , 10.12683548 , 56.53733109 , 2.24 , 14.27 , 50.36 , -32.17
Sheliak , 92420 , 282.51997782 , 33.36266704 , 3.52 , 3.70 , 1.10 , -4.46
Sirius , 32349 , 101.28715539 , -16.71611582 , -1.44 , 379.21 , -546.01 , -1223.08
Spica , 65474 , 201.29824701 , -11.16132203 , 0.98 , 12.44 , -42.50 , -31.73
Tarazed , 97278 , 296.56491454 , 10.61326120 , 2.72 , 7.08 , 15.72 , -3.08
Thuban , 68756 , 211.09729071 , 64.37585051 , 3.67 , 10.56 , -56.52 , 17.19
Unukalhai , 77070 , 236.06697851 , 6.42562699 , 2.63 , 44.54 , 134.66 , 44.14
Van Maanen 2 , 3829 , 12.29124814 , 5.38860956 , 12.37 , 226.95 , 1233.05 , -2710.56
Vega , 91262 , 279.23473511 , 38.78369180 , 0.03 , 128.93 , 201.02 , 287.46
Vindemiatrix , 63608 , 195.54415463 , 10.95915037 , 2.85 , 31.90 , -275.05 , 19.96
Zaurak , 18543 , 59.50735988 , -13.50851533 , 2.97 , 14.75 , 60.51 , -111.34
3C 273 , 60936 , 187.27789142 , 2.05239846 , 12.88 , 3.59 , -11.01 , 4.38
As mentioned in the other answer, the IAU also provides a list of common star names, though not all map directly to a HIP star: https://www.iau.org/public/themes/naming_stars/#n4
Technically speaking, a star name is a proper noun like Vega, Sirius, Antares, Arcturus, Rigel, Betelguese, etc. Vega, for example, has many other designations, most of them catalog numbers, but including Alpha Lyrae, the type of designation you are asking about. With very rare exceptions, only stars visible to the unaided human eye from Earth are given proper names.
A star designation with a Greek letter and the genitive form of the Latin constellation name is called a Bayer designation, since it was first used in the atlas of the heavens by Bayer in 1603. Bayer usually gave the Greek letters in order of decreasing brightness, with Alpha the brightest and omega the dimmest. But Bayer often didn't need all 24 Greek letters for the visible stars in a constellation.
https://en.wikipedia.org/wiki/Bayer_designation
Stars are mostly only given Greek letter designations if they ware visible to the naked eye without optical aid. There are only about 5,000 to 8,000 stars which are sometimes visible to the unaided eye depending on the atmospheric conditions on Earth and the eyesight of the human.
There are only 24 letters in the Greek alphabet, and only 88 constellations in the official lists used by astronomers, and so there can be no more than 2,112 star designations combining Greek letters and the constellation name.
Except that not all constellations have all 24 Greek letters used, and sometimes stars that appear close together as seen from Earth share the same Greek letter with numerical superscripts for each individual star. So the total number of Bayer designations should be different from 2,112.
There are thousands and millions of stars listed in various star catalogs. Most stars in a catalog are known by the name or abbreviation of the catalog and their number in the catalog. Many stars have several different designations ins several different catalogs, and many star catalogs have columns to list some of the other catalog designations of those stars.
Many star catalogs contain thousands of stars without Bayer designations for every star with a Bayer designation. Some may include millions without star designations for each one with a Bayer designation. So randomly searching a star catalog in hope of finding some stars with Bayer designations is a long process.
Here is a link to a Wikipedia table of stars with Bayer designations.
https://en.wikipedia.org/wiki/Table_of_stars_with_Bayer_designations
Most of those stars should have Wikipedia articles. And the articles should list other designations of those stars, which should help you find them in various star star catalogs.
Most stars visible to the unaided human eye from Earth have been given proper names in several different cultures. The International Astronomical Union has a committee on star names, which is working on granting official star names to stars, selecting from the names they have been given in various cultures.
Here is a link to the star names approved so far by the IAU Working Group on Star Names:
https://www.iau.org/public/themes/naming_stars/#n4
The Hipparcos star catalog produced by the Hipparchos satellite contains data on 118,218 stars, so only about 1 or 2 percent of the stars in that catalog should have Bayer designations.
