The name "Tomcat" was originally supposed to be assigned to the Grumman F7F Tigercat, which was primarily a night fighter and "Tom cats", aka male cats, tend to be active and do quite a bit of night time scrapping.
The powers that be at the Navy in the mid 40's however felt the name promoted feline promiscuity and wasn't morally upright enough to befit a Navy aircraft..so the name "Tigercat" was given instead.
Flash forward 25 years to 1969 and the name was brought back both due to Grumman tradition of naming their aircraft after felines (Wildcat, Hellcat, Bearcat, etc) and as a tribute to Tom Connolly who championed the design and the aircraft before congress and the Navy.