I have posted much or all of this in a previous memory - but only once, and it's important.

1. I had forgotten about the HMP SUR Wey when I recently posted on the intriguing co-association of this RN with diuo-nantu "sacred gorges" and other onomastic and archaeological hints that these rivers were holy rivers to the pre-Christian riverains. 
a)
I suggested that the KNT Stour looked a good bet - as a mooted ex-Wye - with gorge at Chilham KNT (sorry no white cattle, that's in Northumb.) - very holy spot at Canterbury - and the PN Wye KNT whatever its origin.
b)
I suggested that the Derbyshire Way might belong in this group (holy spot: Aquae ArNEMET-/Buxton DRB). Gorge.
c)
The Gwent Gwy/Wye has gorges and for sure a holy spot at Tintern (marked by Cistercian abbey). 
d) the BUC Wye - whether or not it is a back-formation from High Wycombe - has the right gorge profile - but lacks any arch. or onomastic clues as to earlier holiness.

d) the clearest example by far is in fact the HMP/SUR Wey.
Holiness indicator in HMP - PN Holybourne (next to Alton, which is a 2ewell" type name).  This of course does look like and I'm sure is - the former name of the trib. stream joining the Wye here.
Holiness indicators SUR - the often commented on cluster of PNs incorporating or prob. incorporating OE theonyms and the like. Peper Harrow SUR.  Thurslow SUR.   Tuesley SUR nr. Godalming.  Maybe even the Godalming PN itself ("if "God" in 1st el). Note Cistercian abbey at Tilford SUR.
The river travels N thameswards thru a gorge at modern Guildford.
This is such a beautiful diuo-nantu that I'd reconstruct this as the former PN here with no other clues - but the Guildford PN may offer a good clue that diuo-nantu (or diuo-dubron, or diuo-ritu even) is the original PN.
I think the Guildford name has been slightly touched up by whoever it was anxious to depaganise the name of this prominent spot (if so, I agree, they didn't bother with Thurslow and Tuesley).
So I posited early OE gieldford "idol/god ford" (/yuh/ at start) bowdlerised towards an anodyne positive sounding "golden" ford (hard g at start) at some time during the Anglo-Saxon centuries.   For gield "idol, etc" see OED s.v. yield and J R Clark Hall s.v. gield.   If you count gold as a colour, this is neochromia - though not by pop. etym - presumably by monastic and so relatively learned re-etymologising.

What is the etymology of these holy Wye/Wey rivers?
I don't know - but I don't think it can be OE weoh "holy" etc. (G Weih-(nachten) etc)
We surely need to look at least 1 language change further (or 2, if Celtic moved to Latin and then OE on the banks of most of these rivers).
Maybe Celtic vesu- "valable, bon, digne" see DLG .   W. "gwiw" - worthy, good.
J Lacroix posits this as the first el. of Vesunna /Perigueux and of the R. Vezere also mainly in the dept. of the Dordogne.
Holiness indicator: the Lascaux cave art. 
Well, that would be longue duree, wouldn't it?
But this is just a suggestion.

Sorry to have needed to repeat myself.   I am glad, Keith, that you enjoyed S. Oosthuizen 2017 (with reserves on some of its linguistic argument).    
Thanks for reading this post. Nick.