In the original, it's B and K, not B and C.
You can see this in the German Wikipedia page (emphasis mine):
Bastian Balthasar Bux ist ein zehn oder elf Jahre alter, in sich gekehrter Junge. Sein Vater hat den Tod seiner Frau, Bastians Mutter, nie verkraftet, flüchtet sich in seine Arbeit und beachtet seinen Sohn kaum noch. In der Schule ist der Junge ein Außenseiter und wird von seinen Klassenkameraden schikaniert. Auf der Flucht vor ihnen rettet sich Bastian in das Antiquariat des Buchhändlers Karl Konrad Koreander.
Presumably Karl Konrad Koreander was changed to Carl Conrad Coreander in the English translation because it looks much more English that way. Carl and Conrad are much more commonly seen as English names than Karl and Konrad, and Coreander would probably look more familiar to an English speaker than the more German-looking Koreander.
So it clearly wasn't designed to be two consecutive letters. As for why they both have triple initials at all, that would make an interesting follow-up question if there is any significance to it, although my gut feeling is that there isn't. The similarity between their names serves to form a (very tenuous) bond between the two, foreshadowing the very end of the book, as well as giving Bastian a point to score over the grumpy shopkeeper:
"My name is Bastian," said the boy. "Bastian Balthazar Bux."
"That's a rather odd name," the man grumbled. "All those B's. Oh well, you can't help it. You didn't choose it. My name is Carl Conrad Coreander."
"That makes three C's."
"Hmm," the man grumbled. "Quite right."