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.
First of all, we say to you: "May Allaah bless you with what He has given you, may you give thanks to the Bestower, may you be blessed with his righteousness, and may he (the child) reach maturity."
We have already clarified in Fatwa 135831 that naming with such compound names is permissible provided that both names are permissible to name with in principle. Nonetheless, it is better to avoid such names as they cause some confusion. Some scholars stated that it is disliked to name with compound names because of this, and also because compound names were not known among the Salaf (righteous predecessors).
Shaykh Bakr Abu Zayd said: "It is disliked to name with compound names such as Muhammad Ahmad and Muhammad Sa‘eed, with, for example, Ahmad being the name and Muhammad being for seeking blessings … and so on. Such compound names lead to confusion; it is for this reason that they were not known among the Salaf; in fact, they were used in the late centuries as previously stated. Similarly, the names added to the Name of Allaah are disliked, such as Hasabullaah, Rahmatullaah, and Jabratullaah – with the exception of ‘Abdullaah, as it is among the most beloved names to Allaah – and (the same thing applies to) the names added to the name Ar-Rasool, like Hasab Ar-Rasool, and Ghulaam Ar-Rasool." [Tasmiyat Al-Mawlood (The Naming of Children)]
The prominent scholar Ibn Jibreen was asked: "Are the compound names that start with the name Muhammad recommended?"
He replied: "These are new names which were not known in the past. Single-word names or names added to other names like ‘Abdullaah, ‘Abdur-Rahmaan, Zayn Al-‘Aabideen and the like have a basis. As regards names that start with Muhammad, like Muhammad Ameen and Muhammad Sa‘eed, such names have no foundation as far as we know but occurred in later generations as a way of seeking blessings in the name Muhammad and the like." [End of quote]
Moreover, if the name of your father is 'Abdus-Salaam, then you should maintain this name when mentioning the full name of your son, or when tracing him back directly to his grandfather. His name will thus be: Muhammad Yoosuf 'Abdus-Salaam, and not Muhammad Yoosuf Salaam, unless one of your grandfathers was named Salaam.
Allaah Knows best.