I believe this may be one of the many customization things ZOS is currently working on (as well as race changes, barber shop etc.) although not sure if it was specifically called out.. so I could be wrong.
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Maybe you can ask some of your friends to report your Char Name as "offensive" and ZoS may give you a chance to change it.
A clever solution for sure, but all reported names are reviewed, so unless it is actually a TOS violation it is unlikely to be changed :P.
Currently there is not a way to change a character's name. If you'd like to see this feature added, please be sure to submit a /feedback at let us know. Thanks for your understanding!