He's number 15.

The War Doctor wasn't the Doctor because he abandoned the promise he made and the name along with it. So, Tennant was the 10th. He didn't fully regenerate that other time in the Meta-Crisis, so he was only/still 10. The Other Tennant is a human, not a Time Lord, and so not the Doctor. Plus, he lives in another universe. The Doctor's Daughter was also a clone and also not a new Doctor, because she wasn't the product of a regeneration.

Then we had Smith, Capaldi and Whittaker as 11, 12 and 13.

13 regenerated into 14 (Tennant again). Then the Bi-generation happened, which again wasn't a regeneration from 14's POV (same face, same personality), but was a full regeneration in that it produced a new Doctor, number 15.

So, they're only a new Doctor if they are a product of a full regeneration, who uses the name 'the Doctor', isn't a clone, is a Time Lord, and isn't a weird spin-off (I'm looking at you, Peter Cushing).

I'm not saying the above makes 'sense' outside of the Whoniverse, but I think it's a reasonably accurate summary of the official position!

• They call Hurt's character "The War Doctor", but as I recall he made the decision himself to not go by "Doctor" because of what he knew he had to do, so it's almost like he abdicated the title.

• The metacrisis doctor was a kind of botched regeneration, which ended up half human (presumably on his mother's side), and thus doesn't count either.

• Tennant's doctor in these three episodes is seen as a distinctly different doctor than 10, just "with the same face", so he counts as 14

• We still don't know whether this bi-generation thing is stable at all. Maybe we won't see David Tennant as often as we think we will.

• Jenny's case is unusual, as she was a clone of the Doctor, who the Doctor treated as his daughter. And you know the inside joke, that the actress who played Jenny (Georgia Moffett) was the real-life daughter of the actor who played the 5th Doctor. And the further meta-joke, which is that David Tennant eventually married the actress who played his clone/daughter.

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.

As far as I understand it, Gatwa is the Fifteenth with the "second Tennant" Doctor being the Fourteenth (distinct from the Tenth). To add even more fun to this, it's been implied that 15 technically comes from a point in the future of the Doctor’s personal time line ("we do rehab out of order") and 14 will properly regenerate into 15 when he has healed his mental and emotional wounds.

Regarding the "Hurt" Doctor, he 'temporarily' discarded the name of the Doctor during the Time War, reclaiming the name "the Doctor" afterwards (hence Eccleston being the 9th). The official name of the Hurt Doctor is "the War Doctor".

As far as confusion, eh it comes with the territory. At this point I let the BBC sort it out 😊

Gatawa is the 15th Doctor. (Even though there are more versions of himself).

In Matt Smith's final episode "The Time of the Doctor", he did acknowledge he was the 13th version of himself, but only the 11th "Doctor". Therefore no more regenerations. (Until the Timelords sent him more)

I have not seen Jodie's run, and can not comment on the storyline from her Doctor.

I did find this article listing all versions of the Doctor. https://www.dexerto.com/tv-movies/doctor-who-every-doctor-and-actor-who-has-played-them-2030888/.

Hope this helps.

In the anniversary series "Once and Future" the Doctor, zapped by a new weapon during the Time War, is being haphazardly "de-generated" through a bunch of his own incarnations, past and future, with their attached knowledge and experience, and at one point