Gentle or to tame
Damyia is likely a modern American creative variation of Damia or Damiana. It is rooted in the Greek word 'damazo', which relates to taming or subduing, often associated with the Greek goddess of forces of nature and growth.
Less common today
Damyia isn't in the latest US Top 1000. It last peaked at #7,154 in 2000.
US births per 5-year period, 1990βpresent (SSA data).