What should we call a subtonic chord in minor scale, VII or the secondary function of III (V/III)? I think, especially in the case of subtonic seventh chord, V7/III- III progression makes more sense than VII7-III because of its dominant function. Any suggestions?
It really depends on the context: in many (most?) cases, it's functioning as the dominant of III, so it would best be labelled as V(7)/III.
But in other instances, it's not functioning that way, so we'll just label it as a VII. The so-called "Andalusian cadence" is one of those times, and we'd just mark it as a VII chord.
VII moving up to i is another story, because someone could interpret the i as a deceptive resolution of the V/III chord. In other words, in C minor, VII to i is B♭ major moving to C minor, which could be read as V–vi in E♭ minor.