...A few days late as I was on holiday
The term "Pesto" in itself is very generic, and indicates many sauces and condiments made crushing together the ingredients in a mortar. (As an adjective, the word "pesto" simply means "crushed" or "beaten")
Which ingredients doesn't matter, as in Italy there are lots of different Pestos, coming from various regions and made of different things...vegetables, nuts, herbs, lard or other fats, meat (I know even a "Pesto d'Asino" made of raw donkey meat, garlic, oil and parsley)
Since the most famous italian pesto is the Genovese one, it has become the "Pesto" par excellence, but its real name is "Pesto Genovese" or "alla Genovese"...I'll update you about the Pesto war for the final answer about the officially admitted ingredients, but it "should" contain ONLY basil, garlic, pine nuts, Parmigiano and Pecorino cheese, salt and EVOO.
If your sauce contains other ingredients (different types of nuts and herbs included) according to the prevalent opinion it cannot be called "Pesto Genovese"...but there's no doubt that it CAN be called "Pesto", ("Mezzaluna Pesto", "Jim Pesto" and so on...

) for the above mentioned reason!
Pongi