Sunday evening in Rome...Perilla?
Yes, definitely reserve at Perilli, especially for Sunday dinner.
I was there on Friday for dinner, and had excellent grilled porcini. But, be forewarned, Sunday at lunch is their big meal of the day, and by the time you get there for dinner, they may run out of porcini.
But I'd agree with Maureen, and suggest Al Ceppo, if mushrooms and truffles are your thing. More upscale than Perilli, so will do those two ingredients in the right way.
Al Ceppo, Via Panama (Parioli), is open Sunday evening and, when mushrooms and truffles are available, does right by them.
Yes, you should reserve, but it shouldn't be necessary very far in advance.
Perilli, not Perilla. Yes, open Sunday evening, but unlikely to have fresh mushrooms, much less truffles. Trattorias do often have fresh porcini, but not truffles.