Hungarian Please Help?

I'm trying to look things up about my grandfather's family! I know both his parents were born in Budapest, Hungary. The last name of my great grandfather was Gyurnek and my great grandmother was Halmose. I've searched Gyurnek every way possible and can't find anything to do with Hungary. I'm wondering if they may have got this name when they came to the US. This last name is very rare in the US. Any Info would be helpful! I've searched the Ellis Island website to see if I could find a listing of when they may have came here, but there is no results for Gyurnek, but there are names that are similar.