Pygmalion was a king of Cyprus who (according to Ovid) carved a statue of his ideal wife and fell in love with it. In answer to his prayer, Aphrodite brought the statue to life and Pygmalion married her. The name, however, hardly seems to relate to this romantic tale, at any rate if it derives from pygme, 'fist' or pygon, 'elbow'.
The only possible suggestion one can make is that Pygmalion made a scale model of his ideal woman, since both pygme and pygon were measures of length, the former being the distance from elbow to knuckles (i.e. just over one foot) and the latter being from the elbow to the first joint of the fingers (i.e. about 15 inches).
The word pygme gave the name of the pygmies, the dwarf peoples of Equatorial Africa. Robert Graves' solution to the name is 'shaggy fist', from pygme and malion, 'hair'. But no shaggy fist comes into the stories about Pygmalion.