(1) You can name only Muhammad. Also you can add some word with it. You can adopt whatever you like.
(2) Abdullah, Abdur Rahman, Muhammad Umar Farooque, Muhammad Abu Bakar, and the names of the sahabah (the companions of the holy Prophet) and pious persons are better. You can choose any of their names.
(3) If you have made Muhammad the part of the name, you should write Muhammad with other name as well.
(4) You can call him only with Muhammad and only with other name as well. It is better to call them with both the names when you have both the names combined.
(5) One is allowed to call someone out of love by adding or deleting. But if one has Allah or Muahammad as part of his name, it is not right to shorten it. For example some one is Abdur Rahman, it is not lawful to call him only Rahman.
(6) It is proved by hadith to name a child on the name of the holy Prophet Muhammad (صلى الله عليه وسلم). It is mentioned in a hadith that the holy Prophet Muhammad (صلى الله عليه وسلم) said:
سموا باسمى ولا تكتنوا بكنيتى . (مشكوة: 407)
(Name after my name, but do not surname on my surname).
Allah (Subhana Wa Ta’ala) knows Best
Darul Uloom Deoband