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 is His slave and Messenger.
It is not permissible at all to name with the names of Allaah that are exclusive to Him, such as Al-Qudoos and Ar-Rahmaan, and the like, regardless of whether they are defined with the definite article 'al' (which means 'the') or not . Please, refer to fatwa 88517.
The scholars stated that the name Al-Muhaymin (The Dominant) is an exclusive Name of Allaah. The book Bareeqah Mahmoodiyyah by Al-Khaadimi reads, “An-Nawawi reported that naming with this name and with the names that are exclusive to Allaah, such as Al-Quddoos, Ar-Rahmaan, Al-Muhaymin, Al-Khaaliq, and the like, is prohibited (haraam).”
Also, Al-Ghunyah, authored by Al-Jeelaani reads, “It is disliked to name with the names that are only befitting to Allaah, the Almighty, such as Quddoos, Ilaah, Khaaliq, Muhaymin and Rahmaan; as Allaah says (what means): {But to Allaah they have attributed partners. Say, "Name them”.} [Quran 13:33]; some interpreters of the Quran said: It means 'Say, 'Name them with My Names and see whether or not this would be befitting for them.''”
It is permissible to name with names that are common to Allaah and to His creatures such as Kareem (Generous), Raheem (Merciful), and 'Aliyy (High), even if these names are preceded by the definite article 'al'. Al-Haskafi said, “It is permissible to name with ‘Aliyy and Rasheed as these are common names, but what is intended in regard to us is not the same as what is intended in regard to Allaah.”
Ibn ‘Aabideen said in his Haashiyah, “It appears that it is permissible even if these names are defined with 'al'.” For more benefit, please refer to fatwa 88517.
Allaah knows best.