Minerva McGonagall turns into a cat. She is an Animagus who can transform into a tabby cat at will.
a cat
Professor McGonagall.
No. There are similar words, for instance one particular fur pattern used to be called a "jellicle cat", a term which appears in Old Possum's Book of Practical Cats and in the musical Cats which was loosely based on it, but Professor McGonagall was not, as far as we know, named after a specific cat variety.
Professor McGonagall is the transfiguration professor at Hogwarts and can turn into a cat. She doesn't follow Harry around though, the cat that does that is Filch the caretakers cat Mrs Norris, who is not a transfigured human.
Minerva sat in her animagi form, which is a tabby cat.
If you are asking about the professors in the Harry Potter books and movies, it is Professor McGonagall, the Transfiguration teacher. She transforms into a tabby cat with markings around her eyes that are similar to her spectacles.
A Bengal cat with a marble coat. They can be either spotted or marble, silver or gold.
Transfiguration was taught by Professor Albus Dumbledore. When he became headmaster he was replaced by Professor Minerva McGonagall.
The first cat we meet is Professor McGongall in her animal form, she is an Animagus which means she can transform into an animal at will.It is also mentioned that the Dursley's neighbour, and Harry's regular childminder, Mrs Figg owns several cats. In the second chapter she trips over one of them and breaks her leg preventing her from taking care of Harry on Dudley's birthday.Argus Filch, the caretaker at Hogwarts, owns a cat called Mrs Norris who wanders around the school and helps catch rule breakers. All of the students hate her.
No animal is mentioned in any of the seven books. She can TURN INTO an animal, though - specifically, into a cat.
Very good question, but this is a book-series for children, so it is never discussed in any of the books.