Thanks for your terrific explanation @Jason Smith.

My knee jerk reaction was to call it an A chord with an F# in the bass. So that would make it A6/F#.

The shape with the F# as the lowest note, the open A string (the minor 3rd) and the E two strings higher than the F# and on the same fret (the dominant 7th) points me to calling it an F# minor 7th.

As you said, looking at the chord in context is key to providing the best name.

There is an underlying lesson here: If you see a major 6th chord, you might be a little freaked because it’s not real common. But you can always play the more familiar minor 7th chord of the relative minor key and you’ll have the same notes.