Character Analysis
Why is his name Mr. Pudding? We don't know. But if this has made you a little bit hungry and you'd like to grab a snack, we'll happily wait for you.
We find out early on that he's the Royal Steward. He's also, in Azalea's mind, "the Royal Stableman, the Royal Boot-Blacker, and the Royal Things-on-the-High-Shelf-Getter" (1.7)—which means he's a pretty useful guy to have around (plus the royal family doesn't have a lot of money, so it's probably better for them to have one person who can do multiple jobs around the castle).
He's apparently been at this for a while, since he seems old. Azalea observes as "with difficulty, he knelt to the floor" (1.7), and she also sees that his hands are "gnarled" (1.9). The fact that he's got "white hair" (6.35) pretty much seals the deal.
We get the impression that he's nice and he genuinely cares about Azalea and her sisters, but he also has to uphold order in the royal household. Like when the King's away and Mr. Pudding catches the girls dancing (thus breaking mourning) yet again, he says, "I can't let you break the rules of mourning, not even for dancing, which I know your mother loved. I'll have to lock the ballroom, misses, and I'm afraid that if I catch y' at it again, I'll feel it my duty to write to your father" (6.38). Clearly tough love is not his style, but he has to keep order somehow.