Someone hacked into my Minecraft account and changed its name

Solution 1:

If you have your web browser to save passwords (or any web browser not on your own computer you used to log into Minecraft's / Mojang's website), you may have had someone else do it easily that way. Also, I would always recommend you never log into any account you are wanting to keep on any computer that isn't yours... ... and never ever trust a not-well-known Minecraft launcher (and totally not a hack client -- those have been known to steal logins and/or infect the system you run it on).

EDIT: Like someone responded to you by comment there, if you have the proof still that you purchased the account, use that when requested by Mojang support.