However I am unsure if there even is a system for renaming yourself, can't recall stumbling upon or hearing about it before - but I imagine it's along the same lines. CO has that option in the cryptic store, not sure if it does in game. So if it's not in yet I imagine it coming when the c-store starts filling up.
Pretty sure you just have to be on the ground rather than in space and you can do it if you have the merits. Though I'm pretty sure this only applies to the formal name, I don't think you can change the short name.