Each diminished chord can have 4 names so what is the rule/convention for determining what to call it - or is there none? It would make sense to me if it were named as the VII chord of the scale/key in which the tune is being played, but that clearly wouldn't work if it doesn't include the 7th note of that scale. Does it depend on the chord inversion, i.e. which note is at the top or which note is at the bottom of the chord?
How about Augmented chords, each of which have 3 potential names?