You’re able to claim and change your surname via the page https://chroniclesofelyria.com/surname-reservation

You’re required to have bloodline+ in order to create and submit a surname, if you’ve done that and you’d like to change it you’ll be required to buy a surname rename from the store ~

As Violet has said, you need to have a bloodline package or higher to reserve a specific surname. Once you have reserved a surname you can change it for $10 if you change your mind.

If you don't wish to pladge for a package that grants surname reservation, then you will be given the surname of whatever family you choose to join when you enter the game.

If you wish to change your forum handle that is also a $10 purchase in the store, but your forum handle isn't linked to your character(s).

Hope that helps!

Or if you meant your forum alias, you can change that in your account management page. You can access that by clicking on your name on the top of the page. There you can click on Alias and change it.
If you don't have alias change available, you can buy one in the merchandise store. (It's a Misc item)

All above are accurate, thanks everyone <3