I think it is pretty typical for kids Peter's age to have imaginary friends, but Peter refuses to do anything in typical fashion. Instead of imaginary friends, my child has named and talks to three of his fingers.
Right thumb's name is Dam. Right index finger's name is Treck. Left thumb's name is Casey.
Casey, Dam and Treck are responsible for most of Peter's bad behavior (mainly hitting his brother, making messes and playing with food), and I frequently find Peter talking to them.
After asking him why only three of his fingers had names, Peter rolled his eyes at me, sighed and said, "Because I am only THREE, MOM! Don't you know that?!?"