Why does this Power Armor appear as X-01 but the parts state T-45?
Solution 1:
Sounds like the Cell reset & Power Armor glitch. Even if you'd made it home with the armor, if you ever exited it, fast traveled, saved (and quit?) and then went back to it, it'd be T-45 parts. Because you don't own the container that is the frame, it gets reset.
Go BUY a frame. Then treat yourself to whatever pieces you find at QAsmoke.
Related: Dude, Who Stole My Power Armor?