I want to start a comic series about my pets living in a universe without humans. This would include their interactions with my neighbors and friends pets. I only use the pet’s first name and the animal’s breed. In one case were I use half of a last name of the owner. Do I need permission?
Yes. If you plan to publish, you should get written permission to create a character based on someone else's physical and intellectual property (their pet's likeness and persona). Otherwise, that person could sue you for infringement and damages.
The Hollywood Reporter has this article about the Grumpy Cat lawsuit.
The Nolo Press has legal self-service resources such as articles and its Getting Permission - Using & Licensing Copyright-Protected Materials Online & Off book that might be useful to you.