The note an octave below middle C is c, followed by d, e, f, g, a, b. Middle C is denoted c', and the notes above it are d', e', etc. The octave above middle C is c''; the octave above that is c''', etc. Roughly speaking, letters followed by one prime are in the first octave of the flute, those with two primes in the second octave, etc.
Sometimes notes are denoted with capital letters, as in "D# key", and in this case I do not mean to imply anything about pitch. The D# key will be used for d'# and d''#, and many other notes. We write "C-foot", for example, just because it looks better than "c'-foot".
The fingers of the left hand are denoted LH1 (the first finger), LH2, LH3, LH4 (the little finger). I usually spell out 'left hand thumb' completely. And the fingers of the right hand are RH1, RH2, RH3, RH4. I do not use these abreviations for keys or holes, just for fingers. The finger holes on a renaissance, baroque, or simple system flute are called 1, 2, 3 (for the left hand) and 4, 5, 6 (for the right).
Keys, whether open-standing or closed-standing, are named for the notes they produce when called into use. Holes are named for the notes that sound from them.
When fingerings for keyless or simple system flutes are described in the text, I give the numbers of the holes that are to be closed and use a dash for holes that are to be left open. For example, 12---- means that (only) the first two holes are to be closed (with LH1 and LH2) and 1234-6 is the "forked F" with only hole 5 open. One can find these fingerings written as, e.g., xxoooo or xxxxox, but, for me, the numbers aid quick comprehension, and sound nicer when said out loud. The D# key can be indicated with "k" as in -23---k for high d''', and other keys can be described in words.
The term simple system flute has been used to mean a variety of things. Some use it for keyless (e.g. Irish flutes) or one-key flutes. But I need a term for the simple form of the 19th century keyed flute (also used in the late 18th and 20th centuries), and will use "simple system" to mean that and only that. For me, keyed flute is somewhat more general, while eight-key flute or Meyer system flute are more specific. See the survey on 19th century simple system flutes, I for a more precise definition of what I call a simple system flute.
When counting keys on a flute, simple system or otherwise, I count every touch, lever, or location designed to be pressed by a finger. I don't care if there are two holes for F, or one, on a simple system flute, but as long as there are two touches, I say there are two F keys; the number of holes is a another matter that can be discussed separately. When counting sections of flutes with tuning heads, I include the head joint proper and the tuning barrel as one section. They are (with some exceptions) kept assembled in cases and not intended to be routinely separated for cleaning.
Some useful information about flute and wind instrument definitions, nomenclature, and misnomers may be found on Wind Instruments in the Dayton C. Miller Flute Collection at the Library of Congress.