your EA account user name is the email address that your account is linked to.
When the new account system went live we all found we had a mysterious new 'user name' and had to do 'lost password' to gain access to it.
When you have the password for your EA account log in to your 'mythic account'.
This was created by EA by adding _uo to your game account user name.
Hypothetical example: Fred has a game account called 'flintstone' which has listed on it the email address 'firstname.lastname@example.org'
His EA user name is therefore 'email@example.com' and his mythic account user name is 'flintstone_uo'. He uses his regular game password to log in to that account. (however this is now a seperate entity and can have its own password, different to your game password)