Gawain Gaiter is Susan Sto Helit's charge as Nanny/Governess in Hogfather. He is brother to Twyla Gaiter and has a large vocabulary for his age. Susan now has him reading Callus Tacticus's journals. He can be unbearably twee, just like his sister, when he wants something, but Susan was weaning him off it. He loved watching the impossible (to adults) happen in front of his child's eyes and used all the ludicrous stories told by their previous governess to have them enacted. For example, in reference to the ancient belief (well - as old as paving stones) that stepping on cracks may summon forth bears to eat you up, Gawain steps on cracks on purpose just so he can see Susan beat them up. A typical child, with all the unthinking cruelty and black-and-white right and wrong that are so characteristic of the under-sevens.
At the end of the events of Hogfather, Teatime's scrying crystal glass eye ended up in Gawain Gaiter's possession, who found lying in the fireplace after Teatime's body had been removed and mistook it for a marble, after with which he would never lose a game with it.
Gawain is a posh prattish name chosen by parents who are vaguely educated in the classics and want a name that shows their offspring as a cut above the ordinary. A Roundworld comparison might be Tarquin or - whisper it! - Homer. Or, to keep the same chivalric theme, Gawain itself or Lancelot. Poor children.
When Death visited Susan at the Gaiters, and asked her "Why Gawain?
", she hazarded "I... suppose it's a good strong name for a fighter..."
"A self-fulfilling prophecy I suspect ," was Death's response. By this he seems to mean that Gawain is going to have to be a fighter because others will ridicule his name and this will lead to the occasional dust-up, especially whilst he is still a child.
Although a variation, or contraction, of the name Gawain is one which is in favour quite a few rungs down the social ladder - Wayne. This has echoes not of an upper-class ponce, but the sort of hard streetwise council estate kid who can barely control a pit-bull terrier on the end of a piece of long string. Gawain could always reinvent himself...