Son of Rhys is right
Like teh de of Frecnch teh Vons in Germany "; in Ireland and Mc MAc in Scotalnd and Slavic suffixes in Cymraeg the prefix is Ap.Ab
The Welsh patronymic system describes family trees in terms of the male line only and records the family association in the 'ap' or 'ab' prefix ('ap' is a contraction of the Welsh word 'mab', which means son). For example, Rhys ap Dafydd translates as 'Rhys, son of David'.
Ap Hugh = Pugh
Ap Rhys = Price
Ap Richard =Pritchard
Ab Evan = Bevan
Ab Owen = Bowen
Ap Ieun/John = Upjohn
Ap Hywel/Howell =Powell
Ap Ros = Prosser
Teh ab ap prefix is itself from mab meanning son as in Mabinogion
These patronymics gradually changed to fixed surnames with Anglicization from Tudor era onwards.
The most common surnames in modern Wales result from adding an s to the end of the name, as in Jones, Roberts and Edwards.
With so many of these plus Davis, Davies and Williams familiar usages evolved
Jones the Butcher
Everna the Post
Harry the Dildomonger
Can 123 the influencer etc