Asuma ISN'T related to Sarutobi.

As somebody already said, Sarutobi is the first name of the 3rd & the last name of Asuma.
If he was even just a relative to either the 3rd or Konohamaru I am pretty darned sure the manga would have shown that already, what's with the 3rd's burial and all.

My guess is that Asuma comes from a ninja family who changed their surname to Sarutobi to honor the 3rd. Doesn't that sound pretty good? It just came to mind.