In my experience Morris Minors tend to be called Moggies whilst Morgans are Mogs. The term Mog is generally accepted, and used, by the Morgan community as evidenced by the number of Morgans sporting MOG plates (mine included). I don't recall seeing any Morris Minors with MOG plates.
I remember having a chat with a chap exhibiting cars at Bluewater a while back who happened to have the initials MOG and told me he couldn't get a decent plate with his initials on it as they had all been snapped up by Morgan owners.
I had a similar problem as I've got EWE on the Mog and I fancied having LAM on my road car so I'd have EWE and LAM. I'd forgotten all about Lamborghini.