Maps aren't written by locals.
For example "Pately Bridge" is known locally as "Pately Brig". Brig being norse for a large rock outcrop - no bridge involved. But some map maker came from the south, asked a local what the place was called and misunderstood the answer.
It's not that "gate" is necessarily pronounced 'yat' - the 'yat' pronunciation is possibly from some totally unrelated earlier word and "gate" is the nearest the official surveyor could come to it (edit apparently in this case yat = gate)
Yorkshire has a wide variety of place names, from early celtic (Pen-y-ghent), mostly Norse, a few anglo-saxon and a scattering of modern Norman places.