1. From Σιμων (Simon), the New Testament Greek form of the Hebrew name שִׁמְעוֹן (Shim'on) which meant "he has heard". This name is spelled Simeon, based on Greek Συμεων, in many translations of the Old Testament, where it is borne by the second son of Jacob. The New Testament spelling may show influence from the otherwise unrelated Greek name Simon.
In the New Testament Simon is the name of several characters, including the man who carried the cross for Jesus. Most importantly however it was borne by the leading apostle Simon, also known as Peter (a name given to him by Jesus).
Because of the apostle, this name has been common in the Christian world. In England it was popular during the Middle Ages, though it became rarer after the Protestant Reformation.
2. Derived from Greek σιμος (simos) meaning "flat-nosed". In Greek mythology this was the name of one of the Telchines, demigods who were the original inhabitants of Rhodes.