I am indeed referring to my partner by his species rather than a nickname.

[And though Hanbei might seem alarmingly impersonal about his small friend, he doesn't hesitate in giving the Pikachu what appears to be a loving enough pat on the head. And the average person wouldn't call a pet their "partner", right? How confusing.]

However there aren't many warriors I know of that do. But the Pokemon themselves don't mind it.