If you follow the current timeline, it should go-
Hurt->Eccleston->Tennant->Tennant->Smith->Capaldi->Whitaker->Tennant->Tennant/Gatwa
Hurt was the real 9th doctor, but we call Eccleston the 9th doctor. And (if I get this all right) Tennant regenerated as himself twice, so he should be the 11th, 12th, 15th and Doctor 16 and a half. But people call him the 10th doctor. And Jodie Whitaker should have been the 14th Doctor, but people call her the 13th Doctor. And then Tennant came back and then there was the bigeneration of him and Gatwa.
And just to add to it all, there's also a female clone of Tennant out there somewhere.
Is anyone else as confused as I am?
EDIT: Oh god, I just realized it gets even more confusing because now there's all the Doctors before Hartnell.
SPOILERS BELOW!
As far as I can tell:
William Hartnell to Paul McGann are Doctors 1-8 in standard order. John Hurt is the 9th incarnation of the Doctor, but is called the War Doctor. Christopher Eccleston is the 10th incarnation, but called the ninth. David Tennant is the 11th, 12th, 16th and possibly co-17th incarnation, but is called 10 or 14. Matt Smith is the 13th incarnation. called the 11th. Peter Capaldi is the 14th (or possibly first of a new regeneration cycle), called 12. Jodie Whittaker is the 15th (or maybe 2nd new) incarnation, called the 13th. Ncuti Gatwa is the co-17th, or possibly third of the second set of Doctors, but is called the fifteenth.
Jo Martin is also some incarnation of the Doctor, but nobody (perhaps even including Chris Chibnall) knows what that's about. Also the rest of the Timeless Child stuff makes this somehow even more of a clusterfuck, but I'm not even going near that one. Also the Curator exists in there somewhere.
@CrabAndBroom @FlyingSquid There's also the Valeyard, which fits in somewhere between the 12th and nth Doctor, as well as Arabella Weir's alternate Doctor, Richard E. Grant's Doctor (who might be an alternate universe Doctor or a future incarnation).
The Children in Need skit can be ignored - as much as I adore Rowan Atkinson in the role - as well as the stage version. And Mark Gatiss, as great as he would be in a legitimate story.