from experience of working in South Wales, I usually use the welsh form - ie without the definitive article. Non-welsh speakers ( who are, after all, around 85% of the population of the Principality ) either don't care either way, or appreciate the gesture, and it saves you a lot of heartburn and general "nuisance value" with those who
do speak it.
15 years ago I wouldn't have done that, but these days the welsh forms are much more widely employed on various forms of documentation. Since I usually take the view that the name of a place is any name by which it can be unambiguously identifed by whoever you are addressing, for the purpose of the exercise, either form will do.
I've followed the same principle in places like the Trans-Caspian - where for practical purposes, place-names are the English version and/or the Roman-alphabet transliteration of the Russian version, where these differ significantly. If the contract is a Russian-language one, I don't need to know anyway, because my Russian isn't sufficient for me to be employed on it.
in African countries I would generally use either the current form, or the current local form plus the former name, where both are still in use or the local form isn't sufficiently known to third parties outside the country
''the stopes soared beyond the range of our caplamps' - David Bick...... How times change .... oh, I don't know, I've still got a lamp like that.