The Family name Minea is of ancient origin. Roman, Greek and Cretan are some possibilities.
There is also the possibility the family name was derived from a locality, that of Mineo, in the Province of Catania, Sicily, Italy.
The name is prevalent on the Italian peninsula and Romania, in Greece (e.g. Mineas), and the former Yugoslavia (i.e. Montenegro) in the form of the Slavicized Minja.
References
Minea Wikipedia(Text) CC BY-SA