I mean, really thinking about it, the reason we don't have names is because of the antartic treaty, we're not allowed to settle there, it's research only and there are very strict rules about what you're even allowed to take there.
So after the melt there will be one of three things:
1. Antartica will remain 100% protected, and will become a haven for a lot of wildlife once the forests regrow, etc.
2. People will be allowed to settle there, once there is soil, trees, etc, maybe there will be new cities and farmlands.
Or a combination of all three! So names could be related to thinking along those lines, also maybe take into account what the new regions geography and climate would be, forests, deserts, mountains, plains, etc... I did have a nice graphic about the predictions but I can't find it now!