A Lexicon of Greek Personal Names (
http://www.lgpn.ox.ac.uk/) includes the Mika in its list
of feminine names found in the Attica region in antiquity. I speculate that the name is
related to "mikro" ("small"). Of course it is a fairly pleasant sounding two-syllable name which is
very likely exist in several cultures with other meanings.
It is probably also being used by some a short for Michaela.