Air Force One is the US Air Force call sign of any plane carrying the President. It happens to be a 747 most of the time, but it could be any airplane he is on. The helicopter that he flies is called Marine One, since it is flown by the US Marines.
It makes no difference who the president is, Air Force One will remain the call sign (also, no plans to replace the current 747)
When President Richard Nixon resigned from office, he flew Air Force One back to his home in California. Half way through the flight, President Gerald Ford was sworn into office, meaning that Nixon was no longer President. At that point in the flight, the pilots had to change the call sign of the plane to another sign other than Air Force One.