Ze was gewend om niet herkend te worden in haar kattenvorm
Zoals opgemerkt door Gallifreyan, verklaart het artikel in Pottermore duidelijk dat ze geregistreerd was voordat ze Hogwarts afstudeerde, en met de hulp van Dumbledore.
By the end of her education at Hogwarts, Minerva McGonagall had achieved an impressive record: top grades in O.W.L.s and N.E.W.T.s, Prefect, Head Girl, and winner of the Transfiguration Today Most Promising Newcomer award. Under the guidance of her inspirational Transfiguration teacher, Albus Dumbledore, she had managed to become an Animagus; her animal form, with its distinctive markings (tabby cat, square spectacles markings around the eyes) were duly logged into the Ministry of Magic's Animagus Registry.
Pottermore - Professor McGonagall
Dus waarom was ze verrast? Omdat ze eraan gewend was dit formulier te gebruiken om volledig onopgemerkt voorbij te gaan behalve haar de Schouwers waarmee ze werkte. Hoewel ze in de buurt was van Perkamentus, werkte ze op dat moment niet voor de Orde.
Minerva McGonagall did not teach the young Tom Riddle, but she was privy to Dumbledore’s fears and suspicions about him. Minerva was not inducted into the Order of the Phoenix during Voldemort’s first climb to power (at that time the Order of the Phoenix was seen as a renegade outfit by the Ministry; successive Ministers feared Dumbledore’s charisma and magical talent, and were inclined to harbour fears that he wished to succeed them). Minerva’s abilities as an Animagus were to prove useful in these dark periods of wizarding history, however, and unbeknownst to her students she spent many nights spying for the Ministry in the guise of a tabby cat, bringing the Aurors crucial information on the activities of Voldemort’s followers.
Pottermore - Professor McGonagall (behind paywall)