Today Mojang introduced the possibility to change your Minecraft nickname, i.e. the name you have ingame. You can change your nickname once within 30 days to one that is free 
.
All you have to do is to migrate your Minecraft account to Mojang, if not yet done, then click on the change link next to your Minecraft nickname on your Mojang account page.
Mojang Account Page
for migrating and changing name
Check whether your desired nickname is free
if you can't log into your Mojang account, have no time for it or whatever
when changing your nick on the Mojang page it'll tell you whether the nickname is free or not of course
make sure to check the hide option, otherwise your search will be displayed publicly
For your information: I'm now Firzen in Minecraft. 
