Transfer character to different account?

I have two accounts, both with my same First and Last name as listed on the account. I was wondering if I could transfer a couple characters from one account to the other. Reason is I don't really like my account name on one of the accounts and would like to transfer characters to the other one. Its not that I don't like the account name, but too many people know it since I use it for most other things like messaging programs, stuff like that.

Or is it possible to change your Account Name? Not the name on the account, but the login name itself.

Thx.