Wrong name on sent emails

I'm signed into the mail app with my gmail account. A few years ago I changed the name on my gmail account and assumed it would be updated everywhere. However I have recently noticed that when I send emails from my iPhone the old name is displayed as the sender. (I noticed because I needed to send some things to a different email account I use for school.) I have done some digging into my gmail account settings and I am sure the problem is not there. Any idea how to correct this?