His favorite was called Puss.
Puss grew presently familiar, would leap into my lap, raise himself upon his
hinder feet, and bite the hair from my temples. He would suffer me to take
him up and to carry him about in my arms, and has more than once fallen asleep
upon my knee. He was ill three days, during which time I nursed him, kept
him apart from his fellows that they might not molest him (for, like many, other
wild animals, they persecute one of their own species that is sick), and by
constant care and trying him with a variety of herbs, restored him to perfect
He wrote quite a bit about Puss and his rabbit compatriots Tiney and Bess. Here's a page with lots about them, plus some Cowper bunny poetry. Here's a stuffed hare - not one of the three - at the Cowper and Newton Museum, itself an interesting destination. He kept his pet hares in hutches in the house hall.