What does it mean to 'call on thy name' in Acts 9:14?
To call on thy name in Acts 9:14 means to invoke Jesus of Nazareth as the Messiah. Ananias reported that Saul had authority from the chief priests to bind all in Damascus who called on Jesus' name, identifying them as believers who acknowledged Jesus as Messiah.
Les explains that Ananias, a believing Jew in Damascus, was approached supernaturally by the Lord from glory. Ananias objected that Saul of Tarsus had done much evil to the saints in Jerusalem, and now in Damascus had authority from the chief priests to bind all who call on Jesus' name. Les clarifies that 'call on thy name' means calling on Jesus of Nazareth as the Messiah. The Lord told Ananias that Saul was a chosen vessel to bear His name before Gentiles, kings, and the children of Israel, and that Saul would suffer greatly for His name's sake. So those who call on Jesus' name are believers who acknowledge Him as Messiah.
And here he hath authority from the chief priests to bind all that call on thy name.