Adding Gmail account to iPhone Mail

When adding a new Gmail account to Mail through settings, I used the Google logo to enter the mail account and password which then appeared to add the account and I can see the mail addressed to that account. However, instead of the email address showing up in the list like the other Gmail accounts (same with other email provider accounts), it simply shows Gmail. This is not good if I ever change another Gmail account as they would wind up with the same name. How to fix this?