Here are some popular Palestinian Arab surnames, and their meaning in English:
al-Masri - the Egyptian
al-Mughrabi - the Moroccan
al-Djazair - the Algerian
al-Yamani - the Yemeni
al-Afghani - the Afghan
al-Turki - the Turk
al-Hindi - the Indian
al-Hourani - the Hauranite (from southern Syria)
al-Kurdi - the Kurd
al-Ajami - the Iranian
al-Shami- the Syrian
Khamis - Bahrain
al-Araj- part of Morocco
Halabi - Aleppo, Syria
Bardawil - named after a lake in Egypt
I have yet to hear of anyone with the surname "al-Filastini."