That has been my experience...for the most part, but not always. That is why there are so many Lebanese with last names like Thomas, Michaels, Peters, Joseph, George, etc...they used their father's first name as a last name here. Of course they are the English versions of those names in the U.S. I have also seen some occupations as last names, such as Khoury, which is an Americanized version of the Arabic name for priest, I believe. (Catholic priests in that part of the world are allowed to marry) I believe Maroon (Marun) is Arabic for Maron as in St. Maron of the Maronite Church.
One other note..often the father's name was used as a middle name for sons and daughters, often more than one in the family would have the same middle name, such as Emily Tony Michaels, or Jean Peter Thomas etc.