The name Anna in the Bible
The name Anna shows up only once in the Bible. She is a prophetess in Jerusalem who testifies about the identity of the infant Jesus, together with a male prophet named Simeon. Both Simeon and Anna are well advanced in years, but of Anna we know that she a daughter of Phanuel of Asher, and that she was a widow whose marriage lasted only seven years (Luke 2:36).
Etymology of the name Anna
Hence it's pretty safe to conclude that the name Anna means Favor or Grace.