How can an anonymous photographer without money hold a personal photo exhibition?

This is more difficult. Unless your work is very good and someone appreciates and sponsors you, you can't even pay the venue fee. In modern society, it is too difficult to do things well without money, especially this thing you mentioned. Or go to public places such as squares and parks and make a small exhibition by yourself. If the management doesn't kick you out, it will be a free personal photo exhibition.