Taken from The Scribes excellent Sega history pages (formerly hosted on SegaBase):
Unfortunately, Sega of America would not be permitted to use the name in its respective market. Another American firm had already registered the term megadrive as a trademark, so Sega's new console was to be renamed Genesis for its U.S. launch. It was a fortuitous choice in retrospect. The name's Biblical connotations would not be lost on conservative-minded American parents, many of whose kids would want to buy the new system. There was also a hidden meaning within the console's new name. Genesis in Hebrew means "in the beginning," and that is exactly what Sega was doing - beginning the nextgen wave of consoles with a Sega system. Up to this point Sega had been playing catch-up to Nintendo.