بسم الله الرحمن الرحيم
(Fatwa: 828/767/SD=8/1438)
(1) Yes, you may keep the name Abidah Fatimah for your daughter. Fatimah is the name of the daughter of the Holy Prophet Muhammad (may peace and blessings of Allah be upon him), while Abidah means a pious and worshiping lady.
(2) It is mustahab to shave the head on the day of Aqiqah, you may shave the head as per your ease whether before the slaughtering the animal or after it.
Allah knows Best!
Darul Ifta,
Darul Uloom Deoband