I personally like this name. It's a nice alternative for the name Mortimer, so you can still apply the nicknames "Mort" or "Morty". Morton is a very decent name for a grown-up man.
Actor Johnny Depp portrays a character named Morton (nickname Mort) in the movie Secret Window. The movie was inspired by a novella by Stephen King called "Secret Window, Secret Garden."
Morton was also the surname of jazz pianist Jelly Roll Morton (born Ferdinand Joseph La Menthe). Born in 1890, he was best known for his hot jazz music and his jazz compositions. He died in 1941.
Mr. Morton was a character in a Schoolhouse Rock short. The purpose of the song "The Tale of Mr. Morton" was to teach children the difference between a subject and a predicate. The chorus of the song, "Mister Morton is the subject of the sentence, and what the predicate says, he does," sums up the song pretty well. Mr. Morton is a shy, sad man in love with Pearl, the woman next door; the song tells the story of their "courtship" of sorts while teaching a little lesson in grammar.