Doctor Who: Did The Timeless Child Just Reveal The Doctor's Name?

Full spoilers for The Timeless Children from here on out. If you haven't watched that then bookmark this, go away and watch the show, then come back here.

So, The Doctor is not originally from Gallifrey. Found as a child standing under a monument of unknown origin that leads to another planet or even universe, she was adopted by Gallifrey's first space explorer. As a child, an accident occurred and she died, causing the first regeneration on Gallifrey. Determined to understand, her mother Tecteun started experimenting with her new daughter's genetic code. In a rather dark scene, we saw that the child didn't survive all of those experiments, causing several more regenerations to occur.

Eventually, Tecteun isolates what she needs and, testing on herself, becomes the first Gallifreyan native to regenerate. She splices this ability into the entire species, limiting it to twelve regenerations each, and effectively conquering death for the already long-lived race of not yet Time Lords.

The Doctor, again last of the Time Lords is now the first of them too. But could the episode have revealed more than that? Could we now have the biggest clue to her name in the entire 57 years of the franchise?

Once envisaged in canon as the way Time Lords fit themselves into other worlds in order to observe history, regeneration got a complete rewrite with this revelation. No longer a mastery of the Time Lords alone, the ability was spliced into the entire race, and it changed their entire destiny.

When Tecteun started exploring, it was heavily implied that she was the first; a familiar tale of a scientist exploring the universe in a rickety ship. But giving each and every person on Gallifrey a set of twelve extra lives emboldened the species. Things like harnessing the power of black holes and developing time travel no longer carried the risk of death, but rather change. And who worships change more than scientists?

Before the rise of the Time Lords, when the fledgling race was still coming to terms with their new ability, the being that brought that change to Gallifrey was still living amongst them. While they were limited in their extra lives, she could live forever. How would these people react to the being that brought them an injection that is effectively a vaccination against death?

How would we?

Before going any further, it's worth mentioning that history is written by the victors, and Rassilon ended up as high president of Gallifrey, so it's safe to say he's the victor here.

In the early days of Gallifrey, before the rise of the Time Lords, the planet was run by a cult devoted to Pythia, described as a great and powerful priestess who was also a merciless dictator. Rassilon and the other founding fathers of Gallifrey were time pilots under Pythia's rule, and he rose to popularity during the war against the Great Vampires. Using this popularity to advance his rationalist movement, Rassilon overthrew the evil priestess and banished all those who worshipped her to the planet Karn where they became known as The Sisterhood of Karn, a group always willing to help out The Doctor.

Knowing what we do now, is it that far of a stretch to think that the cult may have been based around this visitor from another world who had changed the way the entire species existed? Could The Doctor, this figure who literally came from the heavens and brought the dead to life, be the central figure of this cult?

Could the first name she had on Gallifrey be Pythia?