There is no mention of a dog owned by the god Hermes. There is, though, a Chinese company named Hermes Dog, selling various kinds of stuff. Probably they want to be mistaken for the French fashion firm Hermès, who are famous for many products including their 'Hermès Dog Collar'.
If Hermes had a pet it must have been a lamb, because as a boy he spent days tending flocks as a shepherd. You can read about this part of his life in "Hermes the Olympian" a book by David Rosser, available on Amazon.
He had three cats, but they ate each other
In both the Hare and the Tortoise.
Hermes Pan's birth name is Panagiotopoulos, Hermes.
Hermes Bautista's birth name is Hermes Eugene Bautista.
Ben Hermes's birth name is Benjamin Andrew Hermes.
Hermes
Douglas Hermes's birth name is William Frederick Douglas Hermes.
Hermes
Hermes's birth name is Hans Szivatz.
Hermes
Hermes is the Greek name. Roman name: Mercury (Mercurius).
Hermes' Latin name was mercury.
Hermes's roman name is Mercury:)
Hermes Phettberg's birth name is Josef Fenz.