Do we know Kyon's real name? I was just re-watching the anime and it seems like Kyon is only a nickname. Are we ever told what his real name is? Maybe from the light novel? And how come Kyon has such a nickname? Does it have any meaning?
No, we don't.

From quick googling, it seems that it has not been revealed yet, even in the light novel. But it seems some hints exist.

From "Kyon" on Wikipedia:


  The name Kyon is actually a nickname given to him; his real name has yet to be revealed in the series. His sister is responsible for spreading its use amongst his schoolmates, much to his embarrassment and annoyance, and he misses being called Onii-chan (お兄ちゃん, Lit. "older brother") by his sister. In the ninth volume of the light novel (The Dissociation of Haruhi Suzumiya), his real name is hinted at in a conversation between himself and Sasaki, a girl who had known Kyon since middle school, who said that it was a very majestic name that didn't fit him.


His sister's name also hasn't been revealed yet.

Thread in MyAnimeList discussing this - there are many hints and guesses being discussed there.