Changing the 'full name' on an account not working

We have an email address for our office manager position of our small business. It's a position with more turnover than other positions, so instead of using the person's name, we made it "admin@companyx.com". The idea then was to just change the name shown in the 'full name' field when the position turned over.

So I'm trying to change that, and it changes in preferences, but emails that are sent from that account are still showing the old name. It's obviously being stored somewhere. I then tried deleting the account and re-adding it. No change in behavior.

How do I get this change to 'take'?

And FYI, it's a gmail imap account.