Pheobe is a misspelling of Phoebe: the Greek name meaning "bright" or "radiant," associated with the moon goddess and the Titan Phoebe in Greek mythology. The recorded spelling is a registry artifact; the owner almost certainly intended Phoebe, and the extra E was a typo or phonetic spelling.
Registry Artifact Note
Pheobe appears in licensing data as a distinct entry from Phoebe, but it's almost certainly not intentional. Diacritical errors and phonetic misspellings are common in pet licensing paperwork entered quickly at the counter. The actual name in daily use is Phoebe.
Phoebe: The Name Itself
Phoebe is a genuinely lovely name with mythological depth and a well-known pop culture anchor: the cheerful, quirky character from Friends played by Lisa Kudrow. It suits bright-eyed, curious dogs: Border Collies, Jack Russells, Beagles.
The Counter-Reading: The Spelling Will Follow the Dog
Once a misspelling is in the registry, it follows the dog everywhere: vet records, boarding records, ID tags. Owners who notice the error early can sometimes correct it; those who don't may spend years gently correcting well-meaning people who flag the unusual spelling.