Only one account at a time here can be linked to a Facebook account. So, when you logon via Facebook it will always load that same account.
Staff may be able to unlink and allow your new account to be linked or you could just close the first and use a password for the new account.
https://support.chess.com/customer/portal/emails/new
How can I do to remove my username, (patodrez), with which I entered by facebook, given that with him, I see the graphics incomplete. I made a new nickname, but when I log in via facebook, the old nickname with its errors still appears. Thank you very much