SE has said that once version 2.0 hits, those of us with existing characters will have the option to completely re-customize our race, gender, and appearance.

Quote Originally Posted by Square-Enix
The new graphics engine will cause certain objects to display differently than they do in the current version.
Because of this, we will allow all current players the opportunity to re-customize the race, gender, and appearance of their characters upon the implementation of the new engine.
~ from New FFXIV Outline, page 8

When this happens, I plan to change my current female Miqo'te into a male one. However, given that my current character name, Rhianu, is explicitly female, I want to be able to change my character's name to something more masculine to match the new gender.

Also, I want to get rid of my character's surname. Surnames make the character name too long. One name only, please!