"You cannot rename your character's name unless purchased from the C-Store."

When will this, then, be available?

I too would like to know, sounds like an easy fix.

I would like to know as well, really want to rename my character.

Same with me. I thought it would be a simple thing but apparently it is not. I saw where you can change the bio data.

Also...can one alter their character's appearance as well?

You can change your appearance as well as your BO's appearance at SOL Starbase.