Fatema is a variation on the name Fatima, a feminine name of different origins. It can be found as an Arabic name meaning 'Chaste', and is the name of a daughter of the prophet Muhammad. It is also found used in Christianity where 'our Lady of Fatima' is sometimes used to refer to the Virgin Mary.
Anam is a feminine name of Arabic origin and it is said to mean 'A Blessing'. It is found used mainly by Muslim parents who feel their child is a blessing from Allah. The name is not common in Britain but is more popular in India.