Last tested: Sep 14, 2020
If you're connecting via HTTPS, this will be tied to the credentials entered for that connection. Either reset the Git connection with different credentials or take advantage of user attributes to allow multiple credentials.
If you're connecting via SSH, the user on the pull request emails will be the user that initially put the deploy key into the repo from Looker. It's a repo side user, not a Looker user. This post has more context on why our PR system works that way.
So, to change that user, you'll need to delete the deploy key on the repo side, then reset the Git connection in Looker. The user that puts in the deploy key will be the user that shows up on those emails.