Okay, it is finally done! We are live on G Suite - https://gsuite.google.com/marketplace/app/drive_password_password_manager/387000543082
It was a rough (relatively) ride as we got rejected several times because of the name containing Drive. We went back and fourth (even considered changing the name) with them, but at the end of the day, they accepted that this is the name and we are not doing anything wrong wanting to keep it.
In sum - insist on your demands and keep pushing until you get there!