JP C. answered 10/16/19
Expert piano and music theory instruction for all levels and ages!
Hello!
To my knowledge, there are not standard names for your mentioned alterations other than "flat-3" etc. I suppose this is due to the large amount of musical contexts that we may refer to when discussing these notes. In other words, saying the same word may have different meanings to musicians in different cultures or groups. A simple example is saying "dominant seventh" vs C7 (which could also mean the note C in the 7th octave). I would try to keep it is simple as possible, which I suppose is your goal, but be clear about the context or starting point. :-)