All perfect praise be to Allah the Lord of the Worlds. May His peace and blessings be upon our Prophet Mohammad and upon all his family and companions.
The word "Bismillah" is shortened from "Bismillah-ir-Rahman-ir-Rahim," from Arabic, literally: in the name of God, the merciful and compassionate.
Giving this name to a girl is inappropriate for several reasons:
1- This name alludes to "tazkiyat al-nafs" meaning "sanctification" or "purification of the self". The Messenger of Allah (Blessings and peace be upon him) changed the name of a woman from "Barra"(Pious) into "Zainab." This is attested to in the following narration: Muhammad b. 'Amr b. 'Ata' reported: I had given the name Barra to my daughter. Zainab, daughter of Abu Salama, told me that Allah's' Messenger (Blessings and peace be upon him) had forbidden me to give this name. (She said): I was also called Barra, but Allah's Messenger (Blessings and peace be upon him) said: Don't hold yourself to be pious. It is God alone who knows the people of piety among you. They (the Companions) said: Then, what name should we give to her? He said: Name her as Zainab." {Related by Bukhari & Muslim}.
2- Scholars have disliked the name "Ni`mah" (Favor of Allah) because whenever someone asks: Is Ni`mah around? They would say no. i.e. there is no "Ni`mah" around although the "Ni`am" (Favors) of Allah are countless and the same goes for the name "Bismillah." Therefore, if it is said "Bismillah" isn`t around, it is as if it is said ""Bismillah-ir-Rahman-ir-Rahim," isn`t around. In addition, scholars have disliked naming a human being after a verse or a part of it; "Bismillah-ir-Rahman-ir-Rahim," is a complete verse.
3- This is a strange name that could embarrass the girl before her friends and schoolmates. Accordingly, we recommend changing it. And Allah The Almighty Knows Best.