Really, I don't think it would be possible for anyone to forget the most famous pachyderm in Oz, the Elegant Elephant Kabumpo. He's quite possibly Ruth Plumly Thompson's most successful addition to the roster of Oz characters, and one of my favorites as well. He's a very well-defined character, being rather pompous, elitist, convinced of his own rightness, and quick to anger. At the same time, however, he's loyal to his friends, quick with a joke, and so wise that King Pompus, the ruler of his home kingdom of Pumperdink, trusts him more than any of his other advisors. He's been granted the title of Prince and Chancellor of the Realm, and is considered part of the Pumperdinkian royal family.
Kabumpo's origins aren't totally clear. We know that he's the only elephant in Pumperdink or any nearby kingdom (although not the only one in Oz; a few others are mentioned as early on as Wizard), and his first appearance (in Kabumpo in Oz; he's apparently such a prominent character that he received a book title right away) identifies him as a gift to Pompus from from a mysterious stranger at the christening of the King's son, Prince Pompadore. Later books, however, say that Kabumpo was a gift from a celebrated Blue Emperor. This discrepancy provides the main plot idea for Henry Blossom's Blue Emperor, in which the long-forgotten Emperor turns out to be both Pompus' brother and Ozma's grandfather.
The Elegant Elephant's starring roles often involve his being totally convinced of something, only to turn out to be wrong. He thinks that Ozma is the proper princess for Pompadore to marry (Kabumpo), that a dummy with the unfortunate name of Humpy is King Pastoria under enchantment (Lost King), that the Red Jinn lives in the Quadling Country (Purple Prince), and that Toby Bridlecull kidnapped Ozma (Forbidden Fountain). Nonetheless, his heart is in the right place, and he's been willing to put himself into undignified situations when he deems it necessary.
Since the pachyderm is such a popular character, he's appeared in several apocryphal Oz books. I've already mentioned Blue Emperor, and Magic Dishpan introduces his sister Kabina. This elephant isn't really characterized that well, and I've seen it suggested that the author originally just wanted to use Kabumpo himself, but changed it to be on the safe side of copyright. Still, the idea that Kabumpo has a sister with whom he still keeps in touch is interesting. I've considered the idea of King Pompus having his own sister (he already has one canonical and one non-canonical brother, so why not?), and maybe Kabina was a gift from the Blue Emperor to this sister.
By the way, I dressed up as Kabumpo at a few Oz Conventions, as can be seen in this pictorial evidence: