Ok, more accurately, people enter names into our database as an initial., as in they stick in a period. Such as John Andrew Doe becomes Doe^John^A., the period is not part of their name. I agree that its possible that is someone's name, but I am 100% certain that every instance I have encountered is incorrect. The various manufactures software we deal with either get confused by middle names or drop them. They also commonly assume that having 2 names in the first name field means that one is a middle name, and drop it. This isn't useful. I have never encountered someone with a single letter name in my workplace (first, last, anything) and so hadn't considered it. I am confident of this as I compare what every person writes on a form as their name with what our system says.
Some people might find their middle name embarrassing, thus choosing to use an initial to keep it secret where it isn't required for anything but disambiguation.
When the middle name avoids confusion with another person and the situation is medical files its about as important as it gets. There is also a legal obligation for it to be accurate with some if our government contract work. That said, they don't seem to monitor accuracy. I spent a lot of time monitoring it though (checking, correcting, hounding data entry inaccuracy serial offenders), and it still causes me cold sweats every now and again.