Unknown; possibly a modern variation of Damari or Damaris.
Damaree is a rare modern American name. It is likely an invented variant or a phonetic elaboration of Damari, which itself has roots in Greek or Hebrew, or possibly a masculine adaptation of the New Testament name Damaris.
Less common today
Damaree isn't in the latest US Top 1000. It last peaked at #5,864 in 2005.
US births per 5-year period, 1990βpresent (SSA data).