From the Mayberry FAQs
Q. What was the origin of the name Opie? Was it short for something?
A. Jim Clark once told me that Opie Taylor was most likely named for Opie Cates, a prominent bandleader of the '40s or '50s whom Andy Griffith and Sheldon Leonard both admired. I have never figured out if Mr. Cates' name was short for something else, or if it was really "O.P." Opie Taylor did spell his name O-P-I-E. It can be seen on the love note he wrote to Miss Crump in "Opie Loves Helen", and on the board he burned his name into in "Barney's Sidecar." --Paul Mulik
Opie Cates real full name was "Opal Taft Cates"
So there you have it!
You should go back and listen to Two Chairs No Waiting 129: Where Opie Got His Name.
In episode 128, Tim Hollis mentioned that the namesake of Opie Taylor was from a fellow that appeared on the old time radio program “Lum and Abner” following having his very own radio program called “The Opie Cates Show.”
As you may have picked up on, Opie Taylor got his name from band leader and radio actor Opie Cates. On “The Opie Cates Show” (1947-1948), he played a naive unsophisticated person from the country (a.k.a. a rube or hick) getting adjusted to big city life. Cates started each show by saying, “The doggonedest thing happened to me th’ other day,” and then he’d go on to introduce the story for the week. The show never found a sponsor and lasted only 13 weeks.
He then basically moved right over to “Lum and Abner” with the same character in 1949 where he’d tell stories about his hometown of Clinton, Arkansas. Cates appeared on a pilot episode of Lum and Abner that same year but the show wasn’t picked up by the network.
Andy Griffith named Sheriff Taylor’s son after Cates. Both Andy and producer Sheldon Leonard liked Opie Cates so the name was a natural fit.
All I know about Opie's name is, when Steve Quincey started making fun of it - Opie was ready to box his ears in.
My theory is that it was suggested by Dub Taylor, the guy who was the mailman and a few other roles. Dub Taylor was “Opie” in the Dennis the Menace tv show. That could also be where “Taylor” came from.