I am currently reading Paperboy: Confessions of a Future Engineer by Henry Petroski, which I picked up a few days ago in a used bookstore; I'd previously read The Book on the Bookshelf by the same author and enjoyed it.
Petroski talks at one point (p. 114) about a boy named Frank, and he writes:
Frank's full name was Francis Xavier O'Connor, but he never told anybody his middle name. The X in Francis X. was officially the unknown, but nobody who was Catholic could imagine it being anything but Xavier.... Nine out of ten Catholics could guess correctly just from his initials, F. X. O'C., exactly what Frank's full name was"
This reminded me of something that I'd read before, something very similar with the initials F. X. O'B., the O'B standing for O'Brien. It appears that in Word Ways, the "Journal of Recreational Linguistics", in 1968, A. Ross Eckler wrote an article called "The Francis Xavier O'Brien Problem". It used to be available online, and I'd come across it before; I don't know whether Petroski read this or whether he independently came to the same conclusion. The chain of reasoning in both cases is as follows: O'B... hmm, that's got to be an Irish name; O'Brien is of course a very common Irish name. Good Irish Catholics name their kids after saints; Xavier's the only saint anyone's heard of whose name begins with X; the saint Xavier was actually Francis Xavier. If I remember correctly, Eckler claimed that someone initialed F. X. O'B. had a ninety percent chance of actually having the full name Francis Xavier O'Brien. If one Googles "Francis Xavier O'Brien", with the quotes, it seems that it's also common to name one's child "N Francis Xavier O'Brien", where N = Charles, John, James, etc. There are also 157 google hits for "Francis X. O'Brien"; replacing X in turn with the other letters of the alphabet, X is the fifth-most-common middle initial for Francis O'Briens, behind A, C, J, and W. (J is much more common as a first letter for a name than for a first letter of a non-name word.
This raises an interesting question: if you know someone's first and last name, what can you predict about their middle initial? I suspect some predictions can be made; I know quite a few people named either Mary Patricia Irishlastname or Patricia Mary Irishlastname, for example. I've also known two people named at least two people named Katherine Elizabeth Lastname (and both of their last names started with the same letter!). One thing that's clear is that people's names are not independent. If you don't believe me, just answer this question: do you seriously think you might meet someone whose full name is Bela Xavier Sedaris? (Bela Bollobas' Random Graphs and David Sedaris' Naked sit within arms' reach as I write this post.) Certain names correlate with certain ethnic groups, which in turn correlate with certain other names. It's not clear to me immediately whether just knowing someone's first and last initials would give information about their middle initial, but I don't see why it shouldn't.