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 httpwwwleanderarchitecturalcoukimagesphotosfullSignsConwyjpg 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