I have read before that Jupiter is named after the great Roman god because of how bright it is. I can't help but wonder, why wasn't the name given to Venus instead? Isn't Venus much brighter than Jupiter in the night-sky, or am I mistaken?
I don't think this will be a great answer because these are just speculations. I cannot find concrete evidence or sources discussing why Jupiter (the planet) became associated with the "king of gods" and not Venus, but here's my go at citing some potential reasons.
To start, I want to point out that ultimately, we have to trace this back to the Greeks and Babylonians. Sure Jupiter (the planet) is named after the Roman god Jupiter, but really the Roman mythology traces pretty distinctly to Greek mythology and Greek mythology has strong ties to Babylonian mythology. The Greeks were the ones who associated Zeus with the planet Jupiter (and they were likely taking cues from the Babylonians) and the Romans just tagged along with that idea, but changed the god's name. So I think your question then transforms into, Why didn't the Greeks/Babylonians decide to associate the planet Venus with their chief god (being that it is the brightest) and instead chose the planet Jupiter?
Brightness of Venus and Jupiter
First, let's just confirm that Venus is indeed brighter. If you look up the Apparent Magnitude system of Wikipedia, you see a description of how astronomers measure visible brightnesses of astronomical objects (and coincidentally enough, this system was created by a Greek). In this system, smaller and more negative numbers indicate brighter objects. From the table on that page, we can see that the apparent magnitude of Venus varies from $-4.89$ at its brightest to $-3.82$ at its dimmest (this variation is caused by the different configurations of Earth, Venus, Sun positions). For Jupiter, we see that at its brightest it has an apparent magnitude of $-2.94$ and a minimum of $-1.61$. Clearly, even at its brightest, Jupiter is far outshone by Venus at its dimmest. Note that none of this takes into account light pollution or other atmospheric effects which would have been negligible to the Greeks and Babylonians anyway. So we can say emphatically yes that Venus is distinctly brighter than Jupiter, but importantly, we note that Jupiter is still brighter than every other star in the sky $-$ the brightest being Sirius with a magnitude of $-1.47$.
Confusion about Venus
Okay, the Greeks and Babylonians were sitting around looking at these planets and wondering what they were. Likely they started thinking they were big, great deities and started attributing gods to them. I can't say this is a certainty, but one possible reason Venus didn't get the top god was that initially the Greeks and Babylonians weren't even sure Venus was a planet like the rest of the planets were. Because Venus is so close to the Sun, we only ever see it at sunrise and sunset. Otherwise, it is in the sky during the day and dwarfed by the brightness of the Sun. This meant that it took the ancient peoples a long time before they even realized the bright object they saw in the evening was the same as the bright object they saw in the morning. To quote Wikipedia on this:
Observations of Venus are not straightforward. Early Greeks thought that the evening and morning appearances of Venus represented two different objects, calling it Hesperus ("evening star") when it appeared in the western evening sky and Phosphorus ("light-bringer") when it appeared in the eastern morning sky. They eventually came to recognize that both objects were the same planet. Pythagoras is given credit for this realization.
Potentially, the ancient Greeks didn't even consider Venus to be a planet initially. The word planet is Greek and means "wandering star". The ancient Greeks identified objects in the night sky which were different and seemingly more important that the normal stars. However, initially, they don't seem to have grouped Jupiter and Mars in with the same type of object as Venus (and possibly Mercury). Jupiter's motion around the sky may have seemed more grandiose and full of purpose, hence why they attributed it to being their biggest and most important god.
Love and Beauty
As I said, the Babylonians, as well as the Greeks before they figured it out, didn't consider Venus to be a planet, but rather two separate and strange "stars". However, once they figured out the two "stars" were really one and the same and Venus was a planet just like Jupiter, they decided to attribute a proper god or goddess from the pantheon of gods to it. Jupiter was already taken so they had to pick someone else.
Despite that, I don't think the argument that Venus is brighter automatically means it should be the most important god. Note that Venus is named after the Roman goddess Venus (of course) who is also the Greek goddess Aphrodite. This is the Greek goddess of love and beauty and she herself was supposed to be exceedingly beautiful. Venus, the planet, is a beautiful sight to behold and it seems appropriate that the most radiant and beautiful planet be named after the most radiant and beautiful Goddess.
The ancient Mesopotamian astrologers associated each of the known moving lights in the sky (the five planets, sun and moon) with one of their gods. You can see their names, in the case of Babylon, here. The days of the week are all named after these lights, although in English they often use the name of the closest Germanic god. (This practice of associating gods across cultures will become a theme.)
The ancient Greeks learned much from Babylon, but were very much not a culture of religious freedom. Impiety was a crime for which one could be executed in Athens, for example, and importing foreign religion was not allowed in at least some cases. It is therefore unsurprising that when the Greeks borrowed the Babylonian knowledge of the planets, they justified it by replacing each god with whichever Greek god seemed most similar. Nergal, a god associated with war and plague, was for example replaced with the Greek war god Ares. Ishtar, a goddes of love, sex and war, was replaced with Aphrodite. The resident god of Babylon and chief god at the time, Marduk, became Zeus.
Romans, on the other hand, did generally have religious freedom. The ancient Romans in general held the belief that, since the gods they worship are real, similar gods of other cultures must simply be the same gods by other names. It should be stressed that despite this the practices and myths were different, even between Greece and Rome. The Romans therefore thought nothing of calling the planets by the name of whichever god of theirs they felt the Greek name referred to, Venus in the case of Aphrodite.
Having gotten that far, we now need to establish why Ishtar (Venus) is the brightest planet and not Marduk (Jupiter), the chief god of Babylon.
Firstly, Marduk was only in later Babylonian times the chief deity. In earlier periods when Ur was in its prime, the chief god was Sin, the moon god, whose daughter was Ishtar according to Wikipedia. (My copy of Gilgamesh lists Anu as the father of Ishtar. This is likely to have been changed by Babylonian times, in keeping with the local god of Babylon, Marduk, displacing Anu who was father of the gods in Sumerian times.) Marduk was a minor god at the time when the Epic of Gilgamesh was written. In fact, every one of the gods we call the "chief god" was really just the chief god when his city reigned supreme.
Ishtar was also a very fickle goddess. Consider this partial summary of Tablet VI of the Standard Version of the Epic of Gilgamesh, taken from The Epic of Gilgamesh: A New Translation by Andrew George (1999, Penguin, ISBN 0-14-044721-0, p. 47):
Back in Uruk Gilgamesh's beauty provokes the desire of the goddess Ishtar and she proposes to him. Gilgamesh scorns her, reminding her of the fates suffered by her former conquests...persuades Anu, her father, to give her...the constellation Taurus...The Bull of Heaven causes havoc in Uruk...
Furthermore, (p. 223.)
Sometimes she is a mature woman, sometimes an impetuous young virgin.
This fits perfectly with the fickleness of Venus in the sky. It took a long time for humanity to realise that the morning star and the evening star are even the same object, which appears briefly in twilight and even then is sometimes gone (behind the sun). It was very well known in ancient times, for example see Isaiah 14:12 in the Bible, which mentions the fickleness of the morning star. (And is probably the source of the name "Lucifer" for the devil, Lucifer or "Bringer of Light" being an alternative Roman name for the planet Venus.)