Creating a new profile or not does not matter in this case.
If there's a name change whatsoever, you need to have corresponding character names that matches the change in order to connect to the right character on the database.
Simply do:
1. Edit the character's profile, change the name into the new name, press 'Done'
2. Create New Character, type in the 'changed name' for the new character, do whatever adjustment you wish to make, faces, banners, then just log in to a server.