Heh, no. Because in the 172, ATC calls you "Cessna" or "Skyhawk". If they get really confused, you might hear "Skylane".
In the PA28s you get "Piper", "Cherokee", "Warrior", "Archer", and sometimes "Arrow" or "Dakota". Theoretically you could also be a "Cruiser" or a "Pathfinder" as well, but...