On Garm: It is in fact the name of a dog (or possibly a wolf) in Norse
mythology; at Ragnarok Garm will fight against Tyr in front of the cave
Gnipahellir such that both shall slay each other.
Farmer Giles' Garm seems rather less threatening.
Incidentally, Tolkien was not the only modern author to use "Garm" as the name
for a dog: Kipling (e.g. "Garm: A hostage") let one of his trio of
quintessential British soldiers have a dog by this name.
On Galathea: Well, "milk-goddess" is a not entirely inappropriate name
for a cow, especially if she is a good provider on the dairy front.
Tolkien is playing a great deal in this tale with various mythological
traditions: "Garm" points to Norse mythology; but "Galathea" is a Greek name,
and so on.
On giants: They do tend to be proverbially stupid: take the Cyclops in
the Odyssey who asks Odysseus his name and falls for the trick when Odysseus
answers
"nobody."
