To tame or subdue
Damiah is likely a modern feminine elaboration of the Greek name Damian, which comes from the word 'damazo'. It carries the connotation of one who tames or subdues. While rare, it follows the popular trend of adding a soft '-iah' suffix to established masculine roots.
Less common today
Damiah isn't in the latest US Top 1000. It last peaked at #5,371 in 2012.
US births per 5-year period, 1990βpresent (SSA data).