In Scottish the meaning of the name Evan is: Right handed. Welsh Meaning: The name Evan is a Welsh baby name. In Welsh the meaning of the name Evan is: Young. The Welsh form of the Hebrew John, meaning God has been gracious, or God has shown favor.he name Evan is a Hebrew baby name. In Hebrew the meaning of the name Evan is: Stone. American Meaning: The name Evan is an American baby name.