Hmm...this could take a while.

2 dogs:
PJ
Bailey

2 cats:
Pumpkin
Barclay (daughter's pet)

1 bunny:
Thelmer (other daughter's pet)

1 guinea pig
Herbert (other daughter's pet)

Fish:
Data
Lore
Oscar
George
Gracie
Strabo
Spot
Snowflake
Sning
Flea
Tick
Bob

Whew!