Yes, it does. After you've made a character, you can change everything except for it's name afterwards.

Go onto the characters profile then scroll down to the bottom of the page and there should be a modify character link click on that then it should say :
Name : *

Choose which kind of creature it is.
Type : *

Which gender?
Gender : *

Do you allow other visitors to use this character?
Permission to use: * Public (everyone can use the character)
Protected (you can choose the members allowed to use the character)
Private (only you will be able to use this character)

Enter a description of your character (caracteristics, what he/she likes, etc...)
Description :


Then just click on the option of protected or private and then save changes then you should be done.
Hope this helps