Unique, one of a kind; possibly a variant of Monica
Aunica is a rare modern name likely created as a blend of the Latin 'unica' (meaning unique) or as a stylized variant of the name Monica. It carries a sense of individuality and distinction. While its exact etymological path is modern and somewhat obscure, it is often chosen by parents seeking a name that sounds familiar yet remains exceptionally rare.
Less common today
Aunica isn't in the latest US Top 1000. It last peaked at #9,544 in 2003.
US births per 5-year period, 1990βpresent (SSA data).