The common fan fiction idea is that you do not choose your animagus animal. I am not sure what basis if any this has in the Cannon books, much less the somewhat less canonical stuff that Mrs. Rowling has included in the various websites and interviews dedicated to the series. However, we do have one quote that suggests otherwise:
At a recent International Symposium of Animagi, the Uagadou School Team attracted a lot of press when their exhibition of synchronised transforming caused a near riot. Many older and more experienced witches and wizards felt threatened by fourteen-year-olds who could turn at will into elephants and cheetahs, and a formal complaint was lodged with the International Confederation of Wizards by Adrian Tutley (Animagus: gerbil).1
If you do not choose your animal, a school team composed of people who are all dual animagi elephants and cheetahs is not really plausible. My guess is that there are different ways to achieve the animagus transformation.2 If we posit that, then it is possible that the particular method that European wizardry has adopted and/or discovered a method that does include an involuntary choice of animal, and does limit you to a single animal. Being typically arrogant, the British are unwilling to consider that someone else might have a better approach. When it is rubbed in their faces, Mr. Tutley of course reacts with a law suit - if you are better than me, you must have done something reprehensible.
Some writers have suggested that at least some versions of the animagus transformation result in changes to the human, just as there are identifying marks on the animal.3 This would explain Madam Hooch’s eyes.4
Mrs. J. K. Rowling. “Uagadou” Originally published on Pottermore on 2016-01-30. Last Viewed 2021-03-04.↩︎
Others have as well.
- The Mad Mad Reviewer. The Mad Mad Reviewer Published: 2017-12-10. Last Viewed: 2021-11-29.
- CmptrWz. For Want of an Outfit Published: 2021-01-02 Updated:2021-11-26 Last Viewed: 2021-11-29.
works that do this include:
- CmptrWz. For Want of an Outfit Archive of Our Own Published:2021-01-02 Updated:2021-05-14 Last Viewed: 2021-05-14
Mrs. J. K. Rowling. Harry Potter and the Sorcerer’s Stone p. 146. Pottermore Limited. American Kindle Edition.↩︎