YOU are Taylor, the guy you are chasing "Taylor" is another black ops guy who is mentioned in the database and comic.
Basically almost every black ops member is somebody else.
Mind go boom
PC thinks he is Taylor after rebooting because the events of the game already happened to Taylor, in a way.
Your brain got inspired a little bit and made its own story, I guess.
It's also explained in the level loading screen (John Taylor's log) but it scrolls by too fast for you to see.