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 permissible – Allaah willing – to name a new-born child with the compound name consisting of the name Muhammad and the name Al-Mustafa as it is permissible to be named with each of them independently. Combining them does not suggest any forbidden matter in meaning, and it is not possible to forbid a given name unless there is a religious text that prohibits it or that the name includes a prohibited meaning, like being a slave to other than Allaah and the like.
For more benefit on the disliked and prohibited names, please refer to Fataawa 87262 and 82724.
Allaah Knows best.