using world transfer for a name change

[DerpyCubone]

I thought the deal was the only way you change your name is IF the person has the same name as you in that server you picked.
Otherwise, you keep the name anyways.
True or False?

True, when I moved to change my name, I went to a place with that name already on it, prompting a change. When I came back to my real server, there was no one with the new name so I did not have the option to change.