The Series 10 companion is named Bill Potts, but she's a woman. This seems like a very unusual name for a woman. Is this more common in the UK? What is it short for?
From a Radio Times interview with Steven Moffat, about his final episode as showrunner:
How far back did you plan to bring back the first Doctor? In the last series there seemed to be lots of references. For a start you named the companion Bill and her girlfriend was Heather like Bill Hartnell and his wife Heather.
Oh, that was a happy accident. Absolutely accidental.
So you didn’t name Bill after Hartnell – or even after your father, Bill?
No, if she’s named after anyone it’s that I liked the fact that, when we were doing The Day of the Doctor , David Tennant called Billie [Piper] Bill. I thought that was a good name for somebody so I logged it then.
Bill is short for William, which has various female forms, and could be a nod to William Hartnell (who portrayed the first incarnation of the Doctor).
Bill is extremely rare for girls, but Wilda, Wilfreda, Wilhelmina, Willa, Williamina, Willow, Wilma are not rare, and is a much more likely true name, which has been abbreviated to Bill (and this may have been a character choice, influenced by her homosexuality).
Billie is much more common for girls (funnily enough, Rose Tyler, the first companion in the new series, is played by actress Billie Piper).