Ah, now that's interesting, as I've been wondering about these things for Cornish too and there doesn't seem to be an exact consensus. We DO mutate place names if they're Cornish, but also personal names as well. However, I think it's conventional to mutate only personal names of Cornish origin (Peder (Cornish equivalent of Peter) becomes Beder, Briallen ("primrose") - Vriallen, etc.).
At least I hope this is the case, as I happen to have a thing about my own name being fiddled with and if anyone ever mutates me to Gourtenay (second state mutation) — let alone Hourtenay (third) — I will personally bite them.
(I rather like Tesco becoming Nhesco, by the way. We would merely make it Desco, which doesn't sound quite as funny. "My a wra mos dhe Desco" — "I'm going to Tesco." Or it would be Thesco in third mutation, but the only examples I can think of where that would happen are "ow Thesco", "hy Thesco" and "aga Thesco" — "my Tesco", "her Tesco" and "their Tesco". Which I can't quite imagine anyone needing to say in everyday life. )