"مَطْعَم مُحَمَّد جَميل وَغالي."
Translation:Mohamed's restaurant is pretty and expensive.
I see where you are coming from. You want to add (AL) to Mohammed because it is a genitive case between مطعم and محمد, is this the case?
In other situations, you are actually right. But here, it is not the case. Because "Mohammed" is a proper name. We do not add (AL) to a proper name to define it. A proper name is defined by its nature as a proper name.