What happens to our character names when the server ends?

[JaseViator]

After the server ends and we get out characters transferred to Icecrown, what happens to characters that have the same name as other characters on that server? Will we be able to keep our names or will it be a forced name change?

[Obnoxious]

Assuming getting transferred to Icecrown is what in fact happens, the priority is naturally for current characters in that server.
It would be rather ridiculous to have people coming from elsewhere make current players lose their character names.