The basis for this was from Air & Space magazine (Smithsonian September 2006) – a great resource for lots of aviation history.
Since the F4F ‘Wildcat’, Grumman fighter aircraft have had ‘cat’ as part of their nickname or been some type of feline (Jaguar, Panther, etc.). The story of Vice Admiral Thomas Connolly and his support for the Grumman F-14 has become a Navy legend. As the deputy chief of naval operations, Connolly famously testified against the General Dynamics F-111B, countering a powerful Secretary of Defense Robert McNamara, who believed an all-service airplane would reduce cost. The Navy believed the F-111 to be seriously underpowered, and Admiral Connolly testified that: "There isn't enough thrust in Christendom to fix this plane." The F-111B was canceled, and Grumman won a contract to replace it. Historians have written that Connolly's 1966 testimony was a career ender and he never got his fourth star, but it won him immortality in the naming of the F-14. The aviator had flown Wildcats in World War II; his call sign: "Tomcat." Another influential Tom, Admiral Thomas H. Moorer, was the chief of naval operations at the time, and his name may have also helped the cause.
From the Wikipedia entry about the F-14
The ‘Tomcat’ logo was developed in the early 70’s at the request of Norm Gandia, Director of Grumman Business Development and former No. 5 Blue Angel. The Tomcat logo design came when Grumman's Director of Presentation Services, Dick Milligan, and one of his artists, Grumman employee Jim Rodriguez, were asked for a logo by Grumman's Director of Business Development and former Blue Angels #5 pilot, Norm Gandia. Per Rodriguez, "He asked me to draw a lifelike Tomcat wearing boxing gloves and trunks sporting a six-shooter on his left side; where the guns are located on the F-14, along with two tails." The Cat was drawn up after a tabby cat was sourced and used for photographs, and named "Tom". The logo has gone through many variations, including one for the then-Imperial Iranian Air Force F-14, called "Ali-cat". The accompanying slogan "Anytime Baby!" was developed by Norm Gandia as a challenge to the U.S. Air Force's McDonnell Douglas F-15 Eagle.
Following are images of the "Tomcat" logo; the "Anytime, Baby...!" logo; the IIAF "Ali-cat" logo and the "Anytime, Baby...!" logo in French
When the F-14 was retired in 2006 a new Tomcat logo was created to reflect his new role in retirement.