Messenger or angelic
Angelice is an elaborated form of the name Angela or Angelica, ultimately derived from the Greek word 'angelos'. It carries the connotation of a heavenly messenger or a being of divine grace. While rare, it follows the trend of adding the French-inspired '-ice' suffix to classic roots.
Less common today
Angelice isn't in the latest US Top 1000. It last peaked at #7,890 in 2001.
US births per 5-year period, 1990βpresent (SSA data).