The question is complicated by the fact that Puma concolor has over 40 names in English, add to that French, Spanish, and Native names for areas where the cougar, puma, catamount, panther etc lives, then there are names in languages where it does not occur which may or may not be translations of those names.
"Tom" is used for male domestic cats and a few smaller wild cats, but, with large wild cats the familiar name in English for the animal is the term for the male, it is the female that gets a special name: lion-lioness, tiger-tigress. So cougar would be used for the male and cougaress would be the female, but (and this answer is gonna be full of "buts") Onelook.com, which searches over a thousand dictionaries doe not have "cougaress" listed.
Cougar is probably derived from more than one native name, and some of those names refer to different animals; the names and animals were confused by early European explorers. One animal it was confused with was the Jaguar ( which also had several names) The "-ar" ending was added to some of the original names. The word came to English thru Potugese and Spanish, which have a masculine and feminine form of many nouns, ending in -o for male, -a for female, in Spanish. But since cougar is basically a name created in those languages from a native language and passed into English, it does not follow the rules and there may have been gender specific nouns in some of the Native languages.
One name is puma, which at first glance appears to be a Spanish word for the female painter ( yes, painter, from panther), but it too derives from more than one native language. There is no gender specifying form. Some of the over 40 names lend themselves to adding "-ess" mountain lioness, panteress. But the cougar is not restricted to mountains, is not a lion or a panther. Many of the names are localized, Cougar in US Southwest, Panther in southern US, with Spanish forms in Latin America, painter to the upper US South, names with lion to the US West, the West and Appalachia are where most names with mountain in them occur, mountain screamer and even mountain painter. But puma seems to be the term most widely understood in most languages and areas, even if not the most used in local language, and , of course, Puma concolor, is the "scientific name.
Looks like you'll have to use a lion and lioness form for male and female , or actually precede cougar with male or female.
It could be more confusing, you could have asked about the bob cat (Lynx rufus) , in size at least right between the smaller cats, where Tom is used, and the larger ones.
Tom Bob cat sounds like a parody of Southern double names, would the female be a Bobbie Sue cat? Or Rufus and Rufina?
A male coyote is called a dog
It is also known as a yote in certain areas of the country
A young coyote is called a pup or whelp, just like all other canines.
Most commonly called a band, but also referred to as a pack, and a rout.
The male fox is known as a dog fox & the female is a vixen.
Male foxes are known as dogs, tods or reynards, females as vixens, and young as cubs, pups, or kits.
A sub adult.
a laughing sound like a male coyote
Tom
the male rhino is called a cougar.
a pathetic loser.
the name is just male panther or male cougar or puma.
A "Dingo" is the male version of a cougar woman!
The male animal mounts the female. That process is called mating.
the cougar
"Painter" is an archaic name for the puma, also called mountain lion, panther, cougar, and catamount.
Both male and female pumas are called pumas.
The Florida cougar, or panther as it is called there, mainly preys on deer, rabbits, and most any animal it can catch, but deer are their primary prey.
Depends what baby male animal it is.
Ridgil
A male goat.