In one of the less surprising events of the year so far (given alumni relations and fundraising considerations), Princeton is keeping Woodrow Wilson's name on things despite the recent discussion of his vicious (even in the context of his times) racism.
Personally, I'm fine with the last name but would change the first names: Delroy Wilson College, Brian Wilson School. These are two people whose achievements I actually admire.
Less flippantly, I don't know the proper metric for deciding questions such as this. If you're Princeton's president, there are multiple constituencies that you have to think about, and in the long run where you steer the school matters more than these symbolic issues, fraught though they are.
I personally find Woodrow Wilson detestable on balance, and would not want to honor him in any way. But it's a complicated story (history is complicated), as the history of our country is morally complicated (featuring both some very good and some very bad things). I have sympathy for both the Progressive Era legislation of Wilson's first term and the aspirations behind his League of Nations push. But for me personally they're outweighed by the bad.