Asmaa is an indirect Quranic name for girls that means exalted, high, great. It is the name of the daughter of Abu Bakr as-Siddiq, the closest companion of the Prophet, peace and blessings of Allah upon him and his companions. It is derived from the S-M-A root (it became exalted, it became high, he/she named something) which is used in the Quran in a lot of places and the root for words like Samaa’ (sky) and Ism (name).