I don't think there's any problem with naming a theatre after Hal Prince - it's hard to argue with his immense legacy (and as others have pointed out, "The Prince" has a nice, classy ring to it).
As far as optics, I think the problem isn't with the act of naming a theatre after Prince - the problem (in this scenario) is a question of continuing a a tradition of imbalance: naming another theatre after a white man, without making an effort to consider more racially diverse candidates in addition to him. If, for example, we received a Prince theatre and a Hansberry theatre around the same time, I doubt there would be any significant outcry. That's just an example though - it's not like it has to be a strict 1-to-1 quota, it's just about making an effort to consider who might have been left out of the conversation, and acting accordingly.
Part of the problem, too, is that the history of theatre on Broadway has been overwhelmingly white. And a theatre isn't likely to be named after someone who has only been in the industry for 20-30 years. It feels like it has to be a big, lifetime achievement legacy recognition. And the problem is that there are comparatively few POC of Prince's generation who had the footholds to build a legacy on par with his. Many of our most iconic Black theatre artists are either (a) more recent/currently working - and therefor not ready for such a lifetime achievement recognition, (b) more known for their avant-garde Off-Broadway work, not so much for working on Broadway, or (c) were mostly known for 1 big play/musical, and not much else. And all of that is a testament to the way in which Broadway has been a poor nurturing ground for Black talent going back so many decades.
So ultimately, I think we do have a few good candidates of color to receive a theatre named after them - and I think they should get that honor. But in the grand scheme of things, it's probably not the most productive use of time and energy. It seems like it's better to focus on fostering meaningful change at the base level: nurturing a more equitable future and present - allowing space for more producers of color, more writers and directors of color, and possibly even more theatre owners of color (this one seems the most logistically unlikely in this current moment - but hey, we know the Nederlanders have been selling some of their houses this week, so fingers crossed lol!). Re-naming theatres is not an insignificant gesture, but at the end of the day, it's an empty one unless it's accompanied by actual change in the industry.