Gandalf is one of the most recognizable fictional names in English literature, and on a white-coated or silver-muzzled dog, it becomes something approaching destiny. Tolkien's wizard (ancient, wise, dramatically timed in his arrivals, and not particularly concerned with others' opinions) translates to pets with such precision that it's almost not a metaphor.
The White Dog Pipeline
Gandalf the White is the most common reference point for the name's pet use. White dogs (Samoyeds, white Standard Poodles, Great Pyrenees, white German Shepherds) get named Gandalf at a disproportionate rate. The visual mapping is so clean that it almost justifies itself without further argument. An elderly white-faced dog named Gandalf at any dog park is the most correct thing at that dog park. Great Pyrenees are the archetypal fit.
Gray Cats and the Grey Pilgrim
Gandalf the Grey — the earlier, more approachable form — is equally on the table, particularly for gray cats who regard themselves as ancient and inscrutable. A gray cat named Gandalf has clearly earned the name through whatever mysterious experiences comprise a cat's actual inner life.
Counter-Reading: Three Syllables at the Park
Gan-dalf is workable as a recall name, but three syllables at full volume can be a lot when you need a fast response. The obvious short form is Gandy, which is much less majestic but entirely functional. Plan your training approach before the name is on the paperwork. See Gandalf as a name and browse NamesPop for more fantasy options.