But is that a middle name? Do middle names show appended to the first name on the BP, like titles do? One would expect gate agents, even contract ones, to recognize the appendage as being a title...

My wife always puts two middle names separated by a space in the first name field on reservations, rather than the second as middle names. Because she always uses both together, never puts only the first. (She might not even react if one would call her using the first alone.) On the boarding passes the two come attached together.