I couldn't think of many with his name, sorry about that, but I'm sure if you Google 'Horse show names' and then look for ones with 'M' then a lot will come up. It doesn't have to be M either. :)
The ones that I found and like'd were -
Miles of Mystery
Move to The Music
My Kind of Guy
My King of Hearts
My Shooting Star
March to Glory
Melody of Joy
Miracle in Motion
Oh! I just managed to think of a few with Mulligan.
Mulligan in Motion
Mulligan The Mystery
:) Hope I helped and I hope you find one you like. Your horse sounds handsome.
"Anyone who says three's a crowd should get a dog and a horse."
"If Heaven doesn't have horses, I'm NOT going."