Gmail sends with wrong name?

Hello everyone,

I have the following problem:

When I send an email in the iPhone Mail app, it shows the correct name as the sender.

However, as soon as I log into the Gmail app or browser, an old, somewhat embarrassing name is displayed as the sender.

I have already changed the name in the Google settings (it is displayed correctly when logging in).

I also deleted the contact on my phone where the email was saved and created a new one.

Since the name is displayed correctly in the iPhone's regular Mail app, and the problem only occurs in the Gmail app or browser, the solution must be there as well. However, the old, embarrassing name doesn't appear anywhere. Neither in the settings nor in the app. The correct name appears everywhere, but not when I send an email.

I would really appreciate any further advice as I'm starting to get really desperate.