This is because I was talking last night with HE who knows all things in Llandudno, and has lived on the Gt Orme all his life.
The Great Man himself said it was St Bueno's (pronounced Buy-No) as stated by SDQ.
I thought it was pronounced BWEN-O, (but I am a stupid English person so my effort doesn't count)
Dave was quite adamant it should be BEW-No
If no definitive answer can be found, then the GREAT man shall be awarded the prize!
I wonder what Quiggs would say?