AirDrop bizarre problem

I just acquired a MacBook Pro. I can AirDrop from my iPhone to the Pro, but not the other way around. All devices on the latest software.

This Pro is the third Mac we have. My wife's (Pat) Air was purchased new. My former Air was a refurb acquired several years back and AirDrop works with it. When trying to use AirDrop from my iPhone and it sees all three, it shows:

    Pat's             MacBook Air        MacPro's

MacBook Air                              MacBook Pro

Pat is my wife's username and the logged-in user. My former Air is logged-in with my user ID (admin) as is the Pro. My wife's system's admin is my user ID but it is not logged-in.

MacPro WAS a second admin user on the Pro. But it has been deleted completely (attempting to figure this out) yet it still displays. Now my ID is the only admin (and user). I also tried this from my iPad with the same results. 

It seems strange that my former Air does not show (my) user ID above the machine type like the other two. When I logged out of my account into a second admin account (named MacBook) that system does not appear at all!!

It seems my problem is somehow related to the user ID.