The name Ananias comes to us from the Greek Ἁνανίας (Ananías), which itself is a rendering of the Hebrew name חנניה (Ḥananiah). The name חנניה (Ḥananiah) is a theophoric name made up of the Hebrew words חנן (ḥanan), meaning "to favor, be gracious," and the shortened form of the name of the Hebrew deity, יה (Yah), giving us "favored of Yah(weh)" or "favored of the LORD."
Ananias was a popular name and there are several people in the New Testament named Ananias, including Ananias (of the infamous Ananias and Sapphira) in Acts 5, whom God struck dead when he sold a piece of property he owned and retained some of the proceeds from the sale for himself instead of giving the entire sum to the Apostles (and then lied about it to them). There was a high priest named Ananias son of Nebedeus (according to Josephus, Antiquities 20.103), who led the Temple in Jerusalem from 47 to 52 CE. He is described as presiding over the trials of Paul in Jerusalem (Acts 23:2) and Caesarea (Acts 24:1). And then there is Ananias of Damascus, who in Acts 9:17–18 heals the Apostle Paul from his blindness, and about whom Paul says in Acts 22:12, "was a devout man according to the law and well spoken of by all the Jews living there."