You know one thing I always appreciated about Laurel and Hardy? It's that they almost always played characters called "Stan" and "Ollie." Even after they started doing features, they didn't feel a need to make up new character names every time; they were Stan and Ollie, they knew we knew them that way, and there was no reason to call themselves anything else.
Most comedians and comedy teams, especially in features, wouldn't or couldn't try that, so even though they played the same characters in every movie, the writers had to go through this charade of finding new names. If a comedian made enough movies, the writers could conceivably find themselves looking for the 20th or 30th character-appropriate name for the exact same character. Not an easy task.
Sometimes it works. W.C. Fields and Groucho Marx's crazy character names are part of their appeal. And sometimes even a conventional name can work if it's used right. It was usually annoying that Abbott and Costello had to play characters not named Bud Abbott and Lou Costello, but Costello's cry of "Oh, Chuck!" (a substitute, I suppose, for "Hey, Abbott!") became one of the most famous bits from Hold That Ghost.
But usually you wish that the writers would just admit it: like cartoon characters, a screen comedian is always the same character even when the setting changes. Even though Mickey Mouse is a steamboat captain one year and a brave little tailor the next, he's still Mickey Mouse. So why should Dean Martin and Jerry Lewis have to constantly pretend to be someone other than Dean and Jerry?
Obviously, the hardest job in these comedy-team re-namings is coming up with new names for the straight man, the guy who can't have a funny name. It's very hard to remember Zeppo Marx's different character names. And as for Dean Martin, oy. I'm going to list, in random order, the names of Dean Martin's characters from the Martin and Lewis movies.
You will try to guess, without looking at Dean Martin's IMDb listing, which name is from which movie. Betcha can't do it. I certainly couldn't.