Annie Hall question

I was watching Annie Hall again for the umpteenth time tonight, and I got to wondering about why Alvy’s friend insists on calling him Max. It’s not especially funny. And it’s extra weird because that’s HIS name.

There’s a scene in the beginning where the two guys are walking down the street talking and Alvy asks him to stop calling him Max. His friend says, “It’s a good name for you.” And throughout the film he calls him Max, but that one scene is the only explanation.

I’m guessing Woody Allen had some reason for that to be a running gag. Any insights?

According to the webpage below, Woody Allen used to make reservations under the name “Max.” This was back when he, Tony Roberts, and Diane Keaton were on Broadway doing the play version of “Play It Again, Sam.” Tony and Diane would sometimes call him “Max” while eating in the restaurants where he had made those reservations. It became a standard joke among the three of them:

"You know, I was having lunch with some guys from NBC, so I said, ‘Did you eat yet or what?’ And Tom Christie said, ‘No, JEW?’ Not ‘Did you?’…JEW eat? JEW? You get it? JEW eat?"

I LOVE that scene.

According to the Dictionary of Psuedonyms, in 1952 when Allen Stewart Konigsberg decided that he needed a showbiz name his first thought was Max Allen. Max in honor of Max Shulman. Then Mel Allen but he was the Yankees voice. So Woody because it had, “a slightly comic appropriateness and is not completely off the tracks.”