One point relevant to the name change is that the star didn't change. That is, the action never ventured sufficiently far away from the star of Regula that the star of Genesis could be a different star.
We sometimes hear that Trek locations are known by the name of the one relevant planet, sometimes by the name of the star. If the relevant planet changes, then that name probably is the informative one, and the star system now has to go by a different name. And of course the system can go by multiple different names: Ceti Ypsilon system (say), Regula system, Genesis system. Few would have even heard the name of the star or the planetoid before Genesis made the location famous...
The star shining on Genesis is the same as the one for Regula? Source please?