I've done this 2 maybe 3 times now, it's really straight forward and all you need to know is the naming policy for roleplay realms.
Basically, quite a few names aren't allowed on Roleplay names, the main rule is "Non-Medieval/Fantasy Character Names".. So if you have a name like "pwnagemage" etc you can easily get this changed - But if you DON'T have one like that here's my way of changing it.
Simply, have a friend report your name (with a ticket) for non-RP name. USUALLY they don't even investigate the name, but if they do make up something like it's a name of a bunch of racist people from the 1800's and you find it offensive to see the name - 99% of the time they'll have that user change their name - Easy