Afaik, the words Vegan and Vega, have a common root in Proto-Indo-European word "Weg-", meaning "to be strong, to be lively." But the similarity between the words is irrelevant, in that regards. Vega is a direct modernization of the name Wega, whereas Vegan is just a pop culture corruption of "Vegetarian", which in turn has precursors in the form of "Vegetare" and "Vegere", which in turn share the "Vega" common root "Weg-".
Las Vegas, for instance, literally translates to "City of Plantations", a spanish vega is literally a plantation. But the star Vega, on the other hand, has probably nothing to do with plantations, but rather means "lively", because it's such a bright star.