My parents adopted the western practice and gave us his last name, which he doesn’t share with anyone else in his family. It’s Arabic not Hebrew, but I imagine the words are related.
My wife’s last name is in the Domesday book, and they have extensive record of their family’s activities in the U.S.—which is a cool thing you can do when you have surnames! I feel somewhat guilty that the west coast line of the name will die out in favor of a name that has no family significance to anyone, but oh well.
Did your dad choose your last name? (Which, I've read, has a specific meaning in Hebrew, but I'm guessing your family isn't Jewish.)