From the Hebrew name מֹשֶׁה (Mosheh)
which is most likely derived from Egyptian mes
meaning "son", but could also possibly mean "deliver" in Hebrew. The meaning suggested in the Old Testament
of "drew out" from Hebrew משה (mashah)
is probably an invented etymology. The biblical Moses was drawn out of the Nile by the pharaoh's daughter. He led the Jews out of captivity in Egypt and received the Ten Commandments from God.
In England, this name has been commonly used by Christians since the Protestant Reformation, though it had long been popular among Jews.