The early parts of Book 1 may tend toward formulaic plots and thinly veiled morality lessons, but because I came into AtLA expecting “just another kids’ show,” anything that deviated from the “kids’ show” norm was enough to catch my attention… as did this episode.
King Bumi by himself is enough to command a viewer’s attention, since the show’s creators don’t stint with his oddness, his power (as a king or as an earthbender), or his armpit hair. :P He exudes menace–even threatens lives–without being mean about it, and manages to keep everyone off balance with his ability to “think like a mad genius."
In fact, it’s this ability, not his physical presence, that is the most interesting thing about him. It’s the thing that leads him to first conceal his connection with Aang, then exploit it to shake the newly returned Avatar out of his habitual thought patterns. (I think it’s especially interesting that he calls Aang out on his "typical airbender tactic[s]–avoid and evade,” which is the first we hear of the various bending styles having actual philosophical underpinnings!)
In the process–with his brilliant final question, “What is my name?”–he forms the middle link in a pattern that will only grow with this series and LoK. Aang has already demonstrated that he can make new friends quickly, but recognizing friends from a hundred years past is a interesting twist–as is the final link, the Avatar’s ability to form friendships that stretch across lifetimes and will still be benefitting his successor generations later.
In short, I can see why Aang would give this guy’s name to his firstborn son. ^_^