Lord Rees was interviewed recently on the Today programme (BBC R4). The presenter addressed him as Lord riːz. This surprised me, since every bearer of this name that I have ever come across pronounces it riːs, and I’ll bet Lord Rees does too.
The spelling admittedly leads you to expect /z/, as in bees, fees, knees and trees. That is the default for word-final -ees. But this is a Welsh name, so the usual rule does not apply (compare Davies ˈdeɪvɪs).
The origin of the name is the Welsh Rhys r̥ɨːs, r̥iːs. The spelling Rees is only halfway anglicized: compare the fully anglicized variant Reece. The name also came into English as the surname Rice raɪs, which shows it as having been borrowed so early that (in that variant) it underwent the Great Vowel Shift. (The iː forms did not undergo the GVS, so attest a more recent borrowing.)
Latterly, Rhys (with that spelling) seems to have become rather popular as a first name throughout the English-speaking world.
I have the impression that the surname Rees is not nearly as common in the US as it is in Britain. I wonder how it is pronounced there.
The Welsh patronymic of this name, ap Rhys, has given us English Price (borrowed pre-GVS) and Preece (post-GVS).
There are villages in Shropshire called Prees, Prees Green, Prees Heath etc, but I do not know how this Prees is pronounced. According to Wikipedia, its origin is not ap Rhys but a word meaning “brushwood”. That would be Welsh prysg prɨːsɡ̊, which has a voiceless final consonant cluster. (This part of England, Maelor Saesneg, has plenty of Welsh toponyms.)