It is a Flemish (Dutchspeaking part of Belgium) name: (van) Slambrouck, Van Slambroeck, Van Slembroeck, (van) Slembrouck, Slembroeck, Slimbrouck
I found the following online (
http://home.tiscali.be/marcel.vervloet/FpageSe.htm):
Family name derived of the placename Slambroek or Slangebroek (broek = swamp) in several communities (especially in West-Flanders).
Thirza