From my very limited knowledge of Welsh, I think "Y" means "The" and including it in the name makes it tricky to find in an alphabetical list. It is also not used on the pub sign so I suggest it is dropped:

http://www.pubsgalore.co.uk/pubs/56685/

NB - The same comment probably applies to quite a few pubs in Wales, so perhaps another answer is to discount it from searches and lists in the same way as done for "The" in English names?