Usually that kind of names are

(--> those kinds of names are / that kind of name is ;-))

pronounced the former way in America and the latter way in Britain

I would dispute that, insofar as the real truth is that the latter is used by people trying to imitate the pronunciation in the original language (a good thing to do to the extent possible, IMO), and I don't know the distribution of such people in America vs. Britain.

so I'd guess the former

...but this guess happens to be correct in the case of EY himself.