Sheikh Muhammad al-`Arûsi `Abd al-Qâdir, professor at Umm al-Qurâ University
Such compound names are unusual in most Arab countries. However, they are quite common in some non-Arab cultures. names like "Muhammad Shujâ`ah", "Muhammad Sa`îd", and "Sa`îd Sâlih" are rather widespread. These compound names are considered as one name. In Islamic Law, such usages are recognized as permitted customs and traditions.
I do not know any objection to this unless it leads to confusion. If someone says that his name is Muhammad Hasan b. Ibrâhîm Sâlih b. `Alî Hasan, then everyone should know that his grandfather is `Alî Hasan and his father is Ibrâhîm Sâlih. Such names should not be used within cultures where doing so will cause confusion regarding the person's parentage.
In any event, a single-word name is the best way of naming because it does not cause confusion and it is easier in daily discourse, writing, and identification purposes.
Source: Islam Today