Hi there. 
Sorry to say but that's not correct. both names should be on all of the ways. since the Welsh name is dominant, it should go in "name" tag and the English name should go in the "name:en" tag. its up to the renderer which name gets displayed. for example, on this map it only shows English names when available.
https://openmaptiles.org/languages/en/#17.77/51.584364/-3.216985
I've now reverted it to its original name.
If you have any additional questions I would recommend asking on the forums or the discord. I'm active on both. 
Kind regards,
Kits. 