How to select columns that have repeating values from another table in SQLite

I am following Zed Shaw's learnSQLthehardway and I wanted to figure out how to select the names from a table person, who owned multiple pets (pets information in table pet.)

person_pet Table:    

person_id    pet_id
    0           0
    0           1
    1           1
    1           2
    2           3

person Table:

    id        name
     0         Zed
     1         Orange
     2         Limen


pet Table:

    id        name
     0         Jag
     1         Black
     2         Fluffy
     3         Mister

I have been trying to use the COUNT function but I can't seem to get the right results. I must return Zed and Orange based off this data.

SELECT name FROM person, person_pet WHERE id = 
(SELECT person_id FROM person_pet GROUP BY person_id HAVING COUNT(person_id) > 1);

This is only returning Zed and not my name. How? What could solve the problem then?

Any help would be great, thank you!