Before we continue, let's be clear which Atari we're talking about. It's not the original Atari, Inc., Atari Games, Hasbro Interactive, or the company formerly known as Infogrames. This is Atari Corporation, the company started by Commodore founder Jack Tramiel as Tramel (no "i") Technology Limited that acquired certain assets from the consumer division of Atari, Inc. It's the company that brought out the 7800 (to wide release), the Lynx, the ST, and Jaguar.
Programmer D. Scott Williamson, a former employee at Atari Corp's Chicago office, which was in charge of entertainment software at the time, posted some interesting information on the AtariAge forums in 2011:
We were originally hired to write games for the Tomahawk. That was the name that Sega gave their new MegaDrive system for North America. From what I know, Atari VP Larry Siegel had been brokering a deal where I believe Atari would be the North American (possibly worldwide) distributor for the system and its games. Sega was looking for an "aggressive American" name for the console, that's what led to the name Tomahawk, but we didn't like it very much. We had an office contest to see who could come up with a better name, I think the prize was a steak dinner. Steve Ryno came up with the name Genesis, either "as the console that would redefine gaming", or after the effect in the Star Trek 2 movie, either way it stuck. The deal later fell through and I don't know if Steve ever got his prize, but that's is seriously how the Sega Genesis got its name.Former Atari Director of Software Development John Skruch also brought up Genesis and the Chicago office during a 2004 Classic Gaming Expo panel discussion ("Atari: Beginning to End," found here [35:36]).
As for the name Tomahawk, that claim is further corroborated by old Usenet posts, including a copy-paste of a message originally posted by EGM founder/editor Steve Harris on the GEnie service. (This was also allegedly mentioned in EGM briefly, but I cannot find it.)
The deal between Sega and Atari Corp. went pretty far along, according to former Atari Entertainment Electronics Division president Michael Katz, but in the end Jack Tramiel and Sega's David Rosen couldn't agree on terms.