Their Appearance:
* Shih-Terrier: Combining the breeds.
* Rattzu: Short and catchy.
* Tiny Terror: If they're playful and energetic.
* Fuzzy Rat: If they have a longer coat.
Their Personality:
* Sparky: For a lively pup.
* Lucky: For a happy-go-lucky personality.
* Gizmo: For a small and clever dog.
* Patches: If they have a unique coat pattern.
Ultimately, the best name is one that you love and fits your puppy's personality!