Having Two Names, Permissible?
It is mentioned in a fatwa by European Council for Fatwa and Research regarding having names,
There is no legal objection to carrying a compound name… The ways and tradition of the Arabs was for each person, and particularly those of elite stature, to have a name, surname and nickname. For example: `Abdullah, Abu Bakr, and As-Siddiq (all referring to one person), or `Umar, Abu Hafs, and Al-Faruq (all referring to another person). Islam approved of all these names and agnomens.
Therefore, we find no objection to a person, whether man or woman, carrying two names which he or she is known by.
The Prophet Muhammad (peace and blessings be upon him) liked the names that carried beautiful meanings, and he (peace and blessings be upon him) disliked the names that carried bad ones. In such cases he would choose a better name for the person, such as the case when he (peace and blessings be upon him) changed the name of a woman from “`Asiyah” (sinner) to “Jamilah” (beautiful).
The Prophet (peace and blessings be upon him) stated: “The best of names are `Abdullah and `Abdur-Rahman, the most truthful of names are Harith and Humam, and the worst of names are Harb and Murra.”
Thus, there is nothing wrong with using two names for your child. Also, there is no harm with using the two names you mentioned in your question, i.e. Muhammed Abdelrahim.