Was it explained early on? I must have missed the episode. I never hear them call him Gramps or Grandpa. Knowing the character, I'm guessing that he insisted on them calling him, Bub, because Gramps sounds too old.

I believe it's been explained at some point that the name came from Chip, when he was very young -- and apparently just learning to speak. It "stuck" from there.

Note that when Bub's brother Charley arrives and Bub is mentioned, Charley replies "Who?" So as far as family, while the nickname was in use by Steve and the boys in their household, that seems to be as far as it went.

Bub's full name was William Michael Francis Aloysius O'Casey. It was explained in the first episode that Mike had problems saying "Grandpa" as a child and it kept coming out as "Bub." Then everyone started calling him that.

Bub's full name was William Michael Francis Aloysius O'Casey. It was explained in the first episode that Mike had problems saying "Grandpa" as a child and it kept coming out as "Bub." Then everyone started calling him that.
Just like on Leave It To Beaver, the Beaver was called by that name because his older brother, Wally, had trouble pronouncing Theodore when he was born.

Bub's first name changes, though. There was no "William" at the beginning, and Michael was his first name. There's even an episode where Bub says to himself, "Michael O'Casey, what were you thinking?" Or something like that. Then in season 5, Charley shows up asking for "Bill O'Casey".

Bub's first name changes, though. There was no "William" at the beginning, and Michael was his first name. There's even an episode where Bub says to himself, "Michael O'Casey, what were you thinking?" Or something like that. Then in season 5, Charley shows up asking for "Bill O'Casey".
That makes it 2 Michaels. O'Casey and Douglas.

That makes it 2 Michaels. O'Casey and Douglas.

Yup. They also mentioned that Mike was named after his grandfather.

Yup. They also mentioned that Mike was named after his grandfather.
Yeah, that's what I figured. Like Robbie and Katie's triplets were named after him, Uncle Charley, and Steve (Dad).

Bub's first name changes, though. There was no "William" at the beginning, and Michael was his first name. There's even an episode where Bub says to himself, "Michael O'Casey, what were you thinking?" Or something like that. Then in season 5, Charley shows up asking for "Bill O'Casey".
Sometimes, first name changes on TV. Like Fred's boss, Mr. Slate, had different first names on the Flintstones. And I think Eddie Haskell's father had different first names on Leave It To Beaver as well.

I think the names change because someone isn't paying attention to continuity, or no one is assigned the task. On Beaver, yes, Eddie's father was called either George, or Frank.

I can't recall what name appears on the vaudeville poster in Bub's room, visible in several eps, on which he receives billing. It remained on the wall after he left and was seen in one of the early Charley episodes.

Whether William or Michael, the name as printed (in my opinion) should be the preferred or correct name -- but I could be persuaded otherwise.