All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.
We have already issued Fataawa 87262 and 82724 clarifying general conditions for naming a newborn child, so please refer to them.
Also, please refer to Fatwa 123374 where we clarified that it is not permissible to be called a name that only befits Allaah, such as Quddoos, Khaaliq, and Rahmaan, and that if someone is called such a name, he is obliged to change it.
Therefore, it is not permissible for you to use the name Rahmaan as a family name for your daughters. The name Shaheed ar-Rahmaan is also disliked as it involves praising the person called such, and it implies a lie. Abu Hurayrah reported that the parents of Zaynab bint Abi Salamah, named her Barrah (righteous).” The Prophet, sallallaahu ‘alayhi wa sallam, said (commenting on such a name): “Do not ascribe goodness to yourselves. Allaah Knows best the pious among you.” They (her parents) said: “What do we call her?” The Prophet, sallallaahu ‘alayhi wa sallam, said, “Name her Zaynab.”
An-Nawawi said in al-Majmoo‘: “One of the unfavourable widespread situations affecting most of the people, and it occurs in the legal opinion-giving, is the giving of the names "Sitt (Mistress) of People", "Sitt of Arabs", "Sitt of Judges", and "Sitt of Scholars"; what is the ruling on this? The answer is: it is emphatically reprehensible and reprehensibleness of it is derived from the Hadeeth: “The worst name to Allaah is that of a man who calls himself Malik al-Amlaak (King of Kings),” and from the Hadeeth of Barrah changing her name to Zaynab; and because it is a lie.”
For more benefit, please refer to Fatwa 87726.
Allaah Knows best.