I imagine that barns were around before many species were given names, I may be wrong, but barns of varying descriptions have been around for many many years
Possibly the white owl. The earliest recorded use of the name 'barn owl' is in Ray's English Birds, published in 1674. Here's a quote from there, "...the common barn owl or white owl..."
Both words, 'barn' and 'owl' are at least 1000 years old in English with the latter the older of the two. I'd guess that people noticed the whiteness before the barn-ness!
Thanks guys, all good answers, I think Quizmonster`s is the most informative. I`ve also heard them called Rock Owl`s, as they nested in rock faces, cliff faces, before barns were built. Thanks again guys now I can win that pub quiz.