Is it permissible for a male or female singer to open a perfume shop under their name, and is it permissible for a perfume manufacturing company to contract with them to produce a special perfume for them, with the company bearing the costs in exchange for a percentage of the sales, knowing that the singer uses their name and fame in charitable works, and that this use will be for something permissible?

It is forbidden to put the name of a male or female singer on products and sell them, whether for a percentage or not. This is because it constitutes clear assistance in corruption and sin, and an explicit invitation to listen to forbidden things. Allah Almighty says: "And cooperate not in sin and aggression. And fear Allah; indeed, Allah is severe in penalty." (Quran 5:2). There is a difference between a singer using their name for good deeds and another person promoting their forbidden work.