The Japanese name, Junsar, means "police officer". The Jenny officers are often accompanied by Growlithe, to use as a police dog (although there are exceptions, like one had a Spinarak or where another has a Meganium, Parasect and Tangela or one that has the Squirtle Squad, etc.). There are some other minor differences between each of them, but not many as the Joys. The only differences are the symbols in their caps and uniforms (which are different depending on your region). Unova Region Jennies have the back of their hair and their bangs cut.
One Officer Jenny from the Kalos region fell under the control of a rogue Malamar and assumed the identity of Madame X on its behalf. This Officer Jenny had no clue what she was doing, but discovered that Malamar was using her to begin reviving the Ultimate Weapon.
Growlithe is her most used Pokémon along with Arcanine.