Princess Rashidah's son is called: Abdul Raqiib, when you take away all the titles. He's the third and youngest child.
Regarding the name issue, you are right, P. Rashidah would keep her father's name and not take the husband's according to Muslim tradition. The childrens' names have "Bolkiah" in it - but they also take their father's name "Pengiran Anak Haji Abdul Rahim". E.g. the full name of the eldest daughter (minus titles) would be "Raheemah Sanaul Bolkiah binti Pengiran Anak Haji Abdul Rahim". Binti - meaning - "daughter of". I imagine they keep the name Bolkiah to show that they are part of the Brunei Royal Family. Their father doesn't have that name, even though he is a relative, as he is not an immediate part of the family. At formal banquets, he is not allowed to sit with his wife and the other royals even!