Jodie Whittaker https://en.wikipedia.org/wiki/Jodie_Whittaker
Not somebody on my list https://camestrosfelapton.wordpress.com/2017/02/04/the-next-doctor/ but fits the casting habits of Chris Chibnall the new showrunner. Chibnall who had worked on Doctor Who and show-ran Torchwood, had a habit of casting Doctor Who actors in other shows he was involved in (Law and Order: UK, Broadchurch). Consequently, there was some chance that it would be an actor who was in Broadchurch who might be the next Doctor. I was keen for it to be Marianne Jean-Baptiste but apparently not.
For SF fans, Whittaker most notable SF work was Samantha, a nurse who gets mugged and who is then caught up in the alien invasion of a London council estate.
A not-to-adventurous choice. Some quarters (e.g. our old pal Vox Day) are complaining that casting a [gasp] woman will ruin a show they don’t watch. I’m more worried about where Chibnall will take the show than the gender of the actor but a casting decision that suggests some originality is a hopeful sign.