If youre wanting a legitimate business, and intend to file taxes on it and everything, I believe all you need to do is go to your local courthouse of similar building, and apply for an official name.
Im not extremely familiar with Florida law though, so I could be wrong.
I would go to the court house and ask them directly.
Tell them you want to breed and sell legal animals, and ask what you need to do that legitimately.
However...if I were you, I would just do it, and not mess around with paperwork and such.
Now, if you had a large operation going, and were acually going to make money off the venture, then that would be different.
You are not likely to make much or any monies of of a pair of vields though.
That would be as you say, a hobby.
Welcome to the forum! Glad you are here.
Someone may be able to give you better advice that lives and does the same in your state.