Air Force One is the call sign of whatever USAF aircraft (see @slookabill's comment below) the US President travels in. Once he boards another aircraft, the call sign AF1 is transferred to that aircraft (for a dramatic example of this, see the climax of Air Force One movie).
As it is not fixedIf a president were to any one aircraft, if he fliesfly in his 757, it willtheir own aircraft (or commercially) the appropriate ATC call sign would be called AF1Executive One.
TheAs far as fitting out a personal aircraft, the VC-25s are USAF assets (operated by 89 AW) and are highly customised and specifically configured for thisthe job of transporting the president (and support staff), costing over $300 million. I doubt any president is going to get the option of flying their favorite aircraft on a regular basis instead of the state aircraft.
NobodyIt is goingnot likely that the government would pay to configure another (non-USAF) aircraft for the president (The replacement for VC-25 is supposedlyto the 747same specifications as the VC-8)25s serving as Air Force One. After all, no US President's personal car has been configured as the Presidential State Car so far.