I like Jewel and Jurassic! Also, off the top of my head, I can think of
- Jaws (because we all know it's going to be a landshark)
- Jinx
- Jabberwocky
- Jolt
I like this, too! Covet's a great name, and Envy would work, too.
Also, more puppy details, please? Or do we have to wait until she's with you?