We did have a long debate about this on the Talk-GB list and the wiki entry for multi-lingual tagging in Wales reflects the outcome of that debate. That says that in instances where the name is the same in Welsh and English:

"The name: tag should contain the name. It is not, in principle, necessary to add either a name:cy or a name:en (since there is only one name in both languages). However, multi-lingual tagging in Wales is currently patchy. Adding a name:cy tag even though this will duplicate the information in the name: tag would help other mappers distinguish between cases where multi-lingual tagging has not yet been applied and cases where the name is the same in Welsh and English."

That's the process we're following. I'd argue that these are Welsh names as they are the names that are used in Welsh. 

As you identify here we're not mapping for the render since we don't currently render these names. Though we are experimenting with this approach on our pywll tywod server https://pwlltywod.mapio.cymru

We could also render these names without the name:cy tag by using the wikidata entry (we use wikidata to render quite a lot of Cymraeg names already). 

We actively think it is helpful to be unambiguous about the fact that this is the name used in Welsh (as opposed to an English name where multi-lingual tagging has not been applied).