The name was already in the family. It was one of the finalists when the eventual winner, Mustang, was chosen for Ford's ponycar a few years earlier. The name "Cougar" sends a strong message of sleek style and easy gliding, but the powers went another direction in 1964 for Mustang, opting for the speed through the prairie feel.
In retrospect, this allowed for a perfect fit for the next time a need for a name came up. The decision to develop a car in the Mercury product line gave the innovators a chance to improve upon a proven concept. The car-buying public bought Mustangs in record numbers. Now, the company was looking to up the ante with a similar-sized car (as far as perception) with more emphasis on style and comfort. The end result also sold far more than expected.
In reality, the Cougar began well before the Mustang. Known as "T-7," the project to develop this car languished until Ford's Pony bolted out of the gate. Now, with renewed enthusiasm, engineers went to work on T-7. And since no one was using the Cougar name, it was attached to this project. Like the Mustang, the Cougar design came as a result of several teams working independently to come up with the plan.
The design was finalized in early 1965 as a "man's car that a Mustang owner could step up to." Ford believed there needed to be a step between the Mustang and Thunderbird. That part about it being a "man's car" will be addressed later.
The cat was let out of the bag in early 1966. Publicity campaigns started letting the world know of Mercury's plans and the name of the car before the first model was available for sale. The hype leading up to the showroom debut late in 1966 was a multi-pronged effort to fan the fires of the smaller-car buyer.