Let me see if I understand what you are trying to do. You are using the Gmail client app pre-installed on the phone and you are trying to use it to access your Yahoo email account? I've never used Gmail to access any email except Gmail. There is another Email client that can pull POP3 email, but you might actually like the Yahoo Mail apps that are on the Google Play Store better.
I just tried to use it to access my Yahoo email but it said that account already exists. Since I have it installed on the Yahoo Mail app, perhaps it will not allow it to be added to the Gmail client.
Try this...go to the home screen, then hit the Menu button (bottom left on the phone, looks like 3 lines), then hit Settings, then Accounts. This will be a list of all the external accounts configured on the phone. You can change your profile for the ymail account there, add password, change naming, or delet it.