Renamed, or flagged for a name change? Have you tried to log in yet? If you do, you should be prompted to select a new name.
Since you transferred on the same Battle.net account but between two WoW licenses the name technically existed on the destination realm since you had already taken it. As soon as the transfer is complete the naming conflict is resolved, you simply need to rename your character to your original name.
I should note that as long as the characters are level 30 or greater there is no way that another player would be able to take the name. They are reserved for 30 days for the Battle.net account that held it.