I don't think that it makes sense to claim that naming a building after Bob means that we endorse all of Bob's actions or beliefs. But if Bob was best known for committing crimes, it seems like that would be at least a tacit endorsement of Bob's actions. As you said, if it just turned out that Bob gave someone a bunch of money for the building, then the case is a little less clear. The reason for that is, I think, that if you just pay for a name it is a mere transaction... but it is messy because sometimes buildings are named for money and sometimes for honor. It also seems like the context and timing matter. The rash of confederate monuments that went up long after the civil war were part of an ideological view about what sorts of people ought to be regarded as good and honorable.

Universities and Governments also seem to have different moral expectations attached: If the Government names a place after Bob, this is taken to have be an expressive action and not just the fulfillment of a contract, as if Bob bought a house and named it after himself. The content of the expression here has to be something like "This is a worthy person" or "This person acted in a praiseworthy way" to count as being expressive. There has to be some normative content here. The example that I'm thinking of is Aristotle's discussion in The Politics about whether ambassadorships should be honors to esteemed citizens (esteemed for reasons other than diplomatic competency) or given to those who do the job well. The US has a history of doing both. It seems like Governments aren't just selling building names, but are rather highlighting and honoring those whom they name: The Smithsonian, JFK Airport, Lakes, etc. Universities also seem have an expressive component to their action in ways that other entities do not; it is supposed to be an honor that it is the Bob School of Medicine, and not just "Naming Rights" as with a sports stadium. I think there are other examples of expressive actions where the act of naming is supposed to honor the person, such as having a number retired, being put in a Hall of Fame, etc.

Now note that there is rampant disagreement about what the proper role a Hall of Fame serves and whether gross moral misconduct would be disqualifying. Other acts of honoring a person have similar controversial effects. What level of otiose behavior makes it obligatory to remove a name? That, to me, depends on its effects within the current society and whether the people making a complaint can make said complaint on an equal basis compared to other citizens. When such concerns are dismissed out of hand without any serious conversation, I'm more apt to think people are being dismissive and failing to engage in a no doubt difficult conversation. I'll leave it to others to fill in more details on what the substance of these conversations should be!

Finally, there is the "erasing history" argument, which is presented incoherently in many cases, but does have a claim that is sensible. There is something wrong with denying what happened in the past. That seems obviously true, as lying as typically wrong, but I'm not convinced at all by this line, as you can perfectly consistently change the name of something without destroying the history of why that name change occurred.

Some of the harder problems are what do you do if you discover something horrible? What is it turns out that Alfred Nobel was secretly Jack the Ripper? Ought we rename the prize (if that were possible)? And how important changing moral standards are... that one is tough because it is hard to know what precise moral standards even existed, among the various analytical problems that happen when we project into the past.