Answer
This is an official answer by QuranicNames.com Staff
Abeeha means "her father", and it is a shortening of the name Umm Abeeha, which means "her father's mother". It is said that this was the nickname for Fatima, daughter of the Prophet may Allah's peace and blessings be upon him and upon his family. The nickname came from the fact that Fatima used to constantly take care of the Prophet. The name is used mostly by Shi'ite Muslims, however it is also mentioned in Sunni books, such as in books by at-Tabarani and Ibn Hajar al-Asqalani, for this reason it's acceptable for Sunni Muslims as well, though it's not popular.
