All perfect praise be to Allah, The Lord of the worlds. I testify that there is none worthy of worship except Allah and that Muhammad, sallallahu ‘alayhi wa sallam, is His slave and Messenger.
First of all, we say that the scholars stated that it is disliked to give children names added to the name of Allah, except for ‘Abdullah. Shaykh Bakr Abu Zayd said, “Similarly, the names added to the name of Allah are disliked, such as Hasabullah, Rahmatullah, and Jabratullah – with the exception of ‘Abdullah, as it is among the most beloved names to Allah.” [Tasmiyat Al-Mawlood (Naming Children)]
The prohibition is further emphasized if adding the name to the name of Allah gives a bad meaning such as the one mentioned in the question, “Dhiraar Ar-Rahman.” Such a name is hideous! The word Dhiraar means causing harm, as the scholars mentioned; it cannot be added to the name of Allah as such. It should be noted that some of the Companions were named Dhiraar, such as Dhiraar ibn Al-Azwar, Dhiraar ibn Al-Khattab, and others. However, the name Dhiraar Ar-Rahman was not found in the early Muslim generation.
Also, just because a name was that of some Companions does not mean that it is permissible to use it in all cases. There was a Companion named Jahsh (foal; young donkey), Jahsh ibn Ri'aab Al-Asadi; however, scholars held that it is disliked to bear names of animals. Shaykh Bakr Abu Zayd said, “Not all old things are good just because they are old.”
Allah knows best.