Corey Haim during the '80s
Jewlicious has presumed that his last name meant "life."
While the Hebrew word chayim translates as life (as in L'chayim), it is also possible that Haim could have been from the Yiddish word, heim, which means home (as in heimish - - homey, cozy - - or alter heim, referring to the old country/home).
Perhaps Haim was shortened from Haimovitch, meaning the "son of a Hayim". This discussion talks about a Haimovitch family who emigrated from Romania to Montreal and since changed their name to Haines. Perhaps the Haines and Haim family are related, since Corey was raised in Canada. Unless Bernie Haim, Corey's father, wants to chime in here, we'll likely be in the dark.
For now, we're motivated to finally watch Lost Boys, which we somehow missed in 1987.