Ok, so this may be remedial. It is not something I ever worried about much, but I thought I would ask. The rule of thumb is that the chord is named after its lowest fretted note. C for the C that is played on the 3rd fret of the A string etc. And that all makes sense except… In the A chord the lowest fretted note is the E. And in the E chord the lowest fretted note is the B. I guess what I am asking is, am I taking “lowest fretted note” too literally? And, if so, what is actually meant by the term?
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Hi Steven,
Change the word ‘fretted’ in played note, it will become a lot clearer from the OPEN chords… 
I hope this helps for now.
And fretted is your finger on a string in a box/section between those 2 metal pieces/frets on your guitar neck.
Greetings,Rogier
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You are looking through the wrong end of the telescope.
chords are named after their root note.
The chords you are learning are shaped that way on a guitar so that the root note is the lowest note within the chord. Some chords do this by using an open string (chords whose root note is E, A or D) as the lowest note. Other chords whose root notes are not E, A or D have a fretted note giving the lowest root note.
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Chords are named after the root note. Consider the slash chords for example. You will discover inversions at some point as well.
Justin has several theory lessons i think starting Grade 2. You will see how the chords are formed and then change your mind on this. 
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Hi Saint, you are on the right track you just need to look at all notes in the chord rather than just the fretted notes (i.e for the e-chord it is an open e string, a-chord open a string)