Please be sure to pick a name that you like! Once you have selected your name, or have been assigned a random name, there is no way to change it. The name you enter can only be 10 characters or less, and with English-only characters.
If you are connecting the game to your Facebook account, but you don't see the name update to your Facebook name it is because of one of the following reasons:
Your Facebook name is over 10 characters
Your Facebook name has non-English characters
In these cases, your old pirate name will be used.