I'm not real good as this name thing but here are a few I've come up with:
"Therapaws" (for therapy as that's primarily what they will do, provide loving therapy for the patients).
"Helping Paws"
"Palliative Paws" (definition of palliative: Relieving or soothing the symptoms of a disease or disorder without effecting a cure.)
"Paws for Healing"
Good luck! I sure hope you win
