Why is Peter listed as "Ash" in the instructions manual?
People often suspect that it's because his name in the Japanese version may have been Ash, however this is not the case. In the Japanese game his name is Piitaa, which is pronounced as Peter.
One can only assume that they were planning on changing his name to "Ash"... perhaps this relates to the fact that Phoenix are born of fire (and Volcanon is a god of fire), and so when defeated, they are revived from ashes... I don't know ;)
Basically, it's a mistake. They may have planned to change his name, but then after the manuals were printed, they decided not to.