I am wondering if the holes in flutes have a particular name. I am assuming that all wind instruments share the same name for their holes, but I am not sure what it might be.
StoneyB has given you the basics and I mainly agree with him (except I've always spelled tone hole as two words), but here's a bit of illumination.
I am a flutist (you can call me a flautist if you pay me more) and here is a picture of my concert flute, with which I used to play in orchestras when I was younger:
You may be surprised to learn that there are two kinds of holes for that instrument: the tone holes, which are covered by the padded keys, and on certain keys there are holes in the keys themselves. (This is true for clarinets and a few other woodwinds as well, though not saxophones and not the bass versions of woodwind family).
The holes in the keys are there to ensure correct finger posture, and a flute with these "perforated" keys is called an "open-hole" or French model flute.
I have never heard the holes in the perforated keys called "finger holes," but it's possible they are called that in languages other than English. That designation is reserved for a flute that has no (or few) keys, like a Baroque flute, the unkeyed holes of which are called "finger holes" because the fingers directly cover the tone holes.