Whatever plane the President is on, it's radio call sign is Air Force One. That is not the name of the plane itself, just a radio call sign. The president uses one of several different planes. The helicopter radio call sign is Marine One.

Air Force One will remain Air Force One no matter who the President is.

The plane used to transport the President is always called Air Force One, irrespective of which particular plane he's in. It is generally a Boeing 747-200 modified with special equipment such in-flight refueling.

To be more technical, it is Air Force One if he is on an Air Force Plane, Marine One when he is on the helicopter, or Navy One if he is on a Navy plane. The "one" gives the aircraft priority in aviation hierarchy (the smaller the number, the higher the priority).

The current president and his family use air force one

Any airplane carrying the President has the call sign Air Force One.