Efrog doesn't really match its linguistic ties to neighboring English. But is does mean New York (with the 'newydd'). And there's a town in central England named York. So it would just be named Efrog.
Indeed, York is Efrog: https://cy.wikipedia.org/wiki/Efrog
The link is "Eboracum", I think.
Which would probably have turned into something like "Everwick", I think, if the Norse hadn't come and called it "Jorvik" which later became "York" :)
I'd use Caer Efrog for the town of York, and Swydd Efrog for Yorkshire.
Why not just Efrog for York and Sir Efrog for Yorkshire?
York and its parent county Yorkshire are traditionally considered as being in the North of England.
If you glanced at Google/Apple maps etc and thought it looks fairly central, you probably overlooked the Scottish border. The Scots won't thank you for that! :-)
New York, Effrog Newydd, so good they named ot twice! :-) couldn't resist, sorry.
Start spreadin' the news
I'm leavin' today
I want to be a part of it:
Efrog Newydd, Efrog Newydd