From the Wikipedia page of Alpha Ursae Majoris:
Alpha Ursae Majoris, Latinised from α Ursae Majoris, formally named Dubhe /ˈdʌbiː/, is, despite being designated "α" (alpha), the second-brightest object in the northern constellation of Ursa Major.
From the Wikipedia page of Epsilon Ursae Majoris:
Despite being designated "ε" (epsilon), it is the brightest star in the constellation and at magnitude 1.77 is the thirty-third brightest star in the sky.
Why are sometimes the brightest star of a constellation not named Alpha? How many constellations are there with this naming exception?