Well, here's an example: I have two Miqo'te brothers in my linkshell, and at least one of them has taken a traditional Miqo'te name. They both used the Fantasia potions and turned into Elezen, but they can't change their names, which means the one with the traditional name has a name which no longer fits or makes sense for the new character race/tribe.

Maybe make the name change based on what's the most obvious for the old model's given race/tribe. In this case, since the character's first name is what makes them stand out, allow them to change that part but keep the last name. Doing it this way makes it unnecessarily complicated on a system level, though, as opposed to letting them change the entire first and last name.

As noted in previous responses, it updates on lists already if a name changes. And honestly, if it's a friend of yours changing the name, odds are they'll tell you. If it's someone you blacklisted, you shouldn't be concerned, either because the new name still shows up on the blacklist. If it's there, you're probably not going to be dealing with said person anyway, so I'm not sure how their changing names is a problem for you.