I'm trying to understand this but I've not been very successful. For instance, this is a chord I took from something online to demonstrate: 
This is in the Bass clef, no key signature, and called F (Major I assume) but why isn't it C or A?
At first I thought that this would be a duplicate of What determines a chord's name?, but I don't believe it is. That thread discusses chord quality, not actually determining the root!
So: we call these three-note chords "triads," and we name them by what we call the "root" (which is a particular note) and "quality" (which is an adjective like "major" or 'minor"). You can learn about quality in the above link, but as for the root, it comes down to a process that we often call stacking the thirds. Although the chord you listed does have a C and an A in it in addition to the F, we call it an F triad because F is the bottom-most pitch when those three pitches are stacked in thirds.
But before we explain that, we have to first talk about measuring intervals. To measure intervals, simply count the note names from the first to the last. And when we measure intervals in music, we use what we call inclusive counting, meaning we count the first and last note name. So if we're measuring the interval from G to B, we count G ("one"), A ("two"), and B("three"). G to B is thus a third.
Now, back to stacking thirds. Consider the three voicings of this chord shown below:
In the first example, notice that we have a third between A and C (A is one, B is two, C is three), but a fourth between C and F (C is one, D is two, E is three, F is four). These are thus not stacked thirds, so the bottom-most pitch is not the root.
In the second example, we have the same fourth from C to F. Once again these are not stacked thirds, so the bottom-most pitch is not the root.
The last example, however, has a third from F to A and a third from A to C. Since these are stacked thirds, the bottom-most pitch, F, is the root. We thus call this an F triad.
As a shorthand, you'll notice that the stacked-third version (what we call a "root position" chord) has all of the pitches on either a line or a space. So to put a triad in root position faster, simply put all the pitches right next to each other so that all pitches are on a line or space. In the first example above, the F is the odd pitch out, since it's the only pitch on a line while the other two are on spaces. So let's move the F down an octave so that it too is on a space, and voila! We have our root-position triad.
This all leads us to an important distinction in the world of music: the difference between root and bass. The bass is the lowest-sounding pitch. But the root is the lowest pitch when you stack thirds, even though it's not necessarily the lowest-sounding pitch. It's a tricky distinction, but a vital one.
Lastly, you're correct that this is F major, but determining chord quality takes a few more steps. I'll refer you again to What determines a chord's name? if you're interested!
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Thank you for your prompt response, Richard. I have to understand how chords are named and I'm still not clear. There are so many that I don't know how to read and the F chord I used is a good example and nice and simple. I would not know that from the triad as I expect the name of the chord to be the bottom most note. CMaj, eg., I expect to be CEG with C on the bottom. Of course, I can play the notes elsewhere but the name is consistent. If the F chord had been stacked as FAC I would be fine, but as it is, I'm lost. – Janet Hudgins Aug 2 '18 at 5:25
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2The 'all 3 notes on lines or spaces' sums it up perfectly. Couldn't be simpler. +1. Note name rather than pitch? – Tim Aug 2 '18 at 6:57
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I am rather beginner myself so I don't want to play smartass, but isn't it worth mentioning that the same notes can be named differently (and play different function in the composition) depending on the context (=key signature of piece)? For example F G C can be either Csus4 or Fsus2? – Wookie88 Aug 2 '18 at 12:19
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@JanetHudgins Could you maybe clarify what you're still having trouble with? I added in a paragraph about "root vs. bass"; perhaps that will help? – Richard♦ Aug 2 '18 at 15:31
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1@Wookie88 I view that as a discussion of chord quality, which I've intentionally left for the other thread to cover. But you're absolutely correct! – Richard♦ Aug 2 '18 at 15:31
As Richard has explained, the way to determine the root is to move all the notes around (up or down an octave) until they all stack up in thirds, and then the bottom note is the root. In the chord in your example, move the C up an octave to middle C, and they will be in thirds, with the bottom note an F. So, it's an F chord.
The reason that we do it this way (rather than always naming the chord by its bottom note) is that inverted chords, or chords where the root isn't on the bottom, are essentially the same chord as the chord in root position, or not inverted. Displacing a note by an octave doesn't change the quality of it as much as moving notes by some other interval. Try playing your chord, then try moving the C up an octave and playing it again. They will sound similar. Now, try moving the C up one step to D. It is now a D minor chord, and will sound quite different from any inversion of the F chord.
A chord with the third on the bottom (the middle note if the chord is in root position) is said to be in first inversion. A chord with the fifth on the bottom (the top note if the chord is in root position) is said to be in second inversion. Your chord is an F chord in second inversion.
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I do appreciate your time and expertise. I expect I'm not explaining myself well and that's because I don't know as much as you do. – Janet Hudgins Aug 3 '18 at 2:09
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I should add that I'm a senior, took lessons as a child before the revolution, went without for decades but started again several years ago. Now I find it very frustrating that I can't play without sheet music short of memorizing and that's very unsatisfactory. That's what I'm trying to fix--to understand how chords are formed. See next page (character count). – Janet Hudgins Aug 3 '18 at 2:44
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Most of the music I play has chord symbols, also the bass, so I have a choice and I opt for the symbol. That's been part of the whole exercise of switching from notes to chords. But, then I need to know the right chords for the melody. The question I came to you with: how are chords named was because the names don't always clearly relate to the root and I'm not sure how to play it.If I saw the F chord example I used above without the base I would probably play it with the C on top, F on the bottom which is where it sounds best to me.But I would read the bass notes that are there as a C chord. – Janet Hudgins Aug 3 '18 at 2:45
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I do invert or move the notes of chords to a place that's comfortable and sounds appealing. I apologize for dragging this into days. Turns out it's not as easy to put this across here as a personal conversation. You could send me a bill!! ~ ; } – Janet Hudgins Aug 3 '18 at 2:46
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@JanetHudgins Ok. I think you might be confusing "root" with "bass." The point about inverted chords is that the root isn't always in the bass, which is the bottom note. The chord is in "root position" when the root is in the bass, and if it isn't in root position the root is not in the bass. If you have a chord symbol and a bass note, you do not have a choice between the two. The bass note will be one of the members of the chord, and you need to fill the other voices with other members of the chord. (This oversimplification avoids mention of "non-chord tones"; I would save that for ... – BobRodes Aug 5 '18 at 0:03
