Problems setting up name and photo in Messages

I would like to make use of the new “Share Name and Photo” feature in iOS 13, but when I try to go to that setting in the Messages app or in Settings > Messages, I get an error saying “Sharing name and photo is not available because multiple phone numbers are associated to your Apple”.

Originally this made sense because I did actually have multiple numbers associated with my Apple ID, but I have removed one of them and I’m still getting the error.

I have confirmed that there is only one phone number listed in:

• Settings > Apple ID > Reachable At
• Settings > Messages > Send & Receive
• Settings > FaceTime

Why does it still tell me that I have multiple phone numbers associated with my Apple ID? Has anyone else had this problem trying to get the Share Name and Photo feature working?

I should note that I do have multiple email addresses associated with my Apple ID, but I have seen no indication that this is the problem.