What are the fins near the tail of a helicopter called?
You can call them horizontal and vertical stabilizers, since that is exactly what they do, in forward cruising flight.  The vertical stabilizer is there because the tail rotor itself doesn't provide as strong a weathervane effect as a fixed surface. So it stops the nose from oscillating left and right in forward flight same as the stabilizer in an airplane.  

The horizontal stabilizer is to provide some down force to keep the body angle a little more level in cruise flight.  The rotor disc is flying along doing its thing with this big weight under it, which wants to swing back and pitch the nose down from air drag and the forward movement of the suspension point (more or less like running along with a tennis ball suspended on a string - it swings back and stays at an angle until you stop running).  The horizontal stabilizer's down force counteracts some of this and helps dampen pitch oscillations and keep the nose at a more desirable (higher) attitude.