What is the legitimate name for a girl: Is it the name given at the ‘aqiqah (Shayma), or the name officially registered in documents (Khadijah)?

The legal name is chosen by the parents, and it is permissible to change it if there is a need for a better name, especially if the name is disliked. There is no harm in the names "Shayma" and "Khadijah," as Shayma was the Prophet's foster sister (peace be upon him), and Khadijah was the Prophet's wife (peace be upon him). The matter is flexible regarding keeping the name or changing it.