If you just made the character I'd say scratch and remake
with a slightly different name or a space on the front. Then there are two things you have to do:
1. Post in your character approval forum with the new name (For documentation purposes)
2. Post in the character deletion thread for the deletion of the character you messed up (Character deletion thread is in the Character Approvals Forum. Be sure to add Bioware (Login) Name, Character name, and reason ).
If you have gained sufficient levels with the character , then you can ask for the bio changed in the Disputes and Grievances section. Be sure to format your post the way the GMs would like it. Its outlined in one of the stickies in the thread.