I think I can tell A from D from E when I play them but listening to it through the computer was hard. Maybe I need to crank the volume.
If you're talking about just hearing a single chord played - most people can't tell what chord (or note) it is. Those who can have what is called 'perfect pitch'. That's something you're born with; it can't be learned.
What you can do is learn 'relative pitch'. That's where you hear the first chord and you know it's A. Then you can tell what the next chord is by how much higher or lower it is than the A chord. Or even if you don't know what the first chord is, if you call that the I chord, you'll be able to figure out the progression, even if you're not sure what key the song is in.
Note: if the E, A, and D chords are played with 6, 5, and 4 strings respectively - that would be something your ear could pick up on - but that's not the same thing as hearing and knowing the notes.