All the men on my dad's side of the family have the same middle name, with just a different first name.

It's apparently not an uncommon tradition in several areas of the world to either have either the first or middle name be shared, and then a unique name for the unmatched one (e.g. John Alan Doe, John James Doe, John Matthew Doe - Alan John Doe, James John Doe, Matthew John Doe).

Eastern Europe of the Slavic variety enters the chat with a concept of patronymics. Nobody asks you if you want to have a middle name, it's always a deriative of your father's, by law.

My son was born in a country with doesn't write those in a birth certificate. When we went back, guess what -- they still added it by deriving it from my name.

Possibly. I’ve just heard it more with girls and wouldn’t expect it’s evenly common on relative basis but certainly could be wrong

My children have no middle name, and neither did I or my brother.