Also short for Finley/Finlay. I think that's where its "common-ness" comes from as about 10 years ago, every second boy was Finley.
If this sort of thing bothers/interests you, ask yourself, "William is in the next room, how old is he?" then substitute it for "Finn".
For me, I'd have no clue how old William was, because as pps have said, it's timeless. Finn would definitely be a child.
(eg how old is Charlotte? - who knows...how old is Ava? Ava is either 85 or 3
)