The spelling "Conway" has fallen out of modern usage in English and is considered old fashioned. Similar to how Y felinheli is no longer referred to as "Port Dinorwic". The name is de - Anglicised. Here is the welcome sign for Conwy. http://www.leanderarchitectural.co.uk/images/photos/full/SignsConwy.jpg As you can see the spelling "Conway" is not on the sign. Which means that "Conwy" is the spelling used officially for both Welsh and English.