I put off weighing-in on this debate yesterday, but I've decided to do so today.
The differences in orthography (what letters you use to represent a sound) between English and Welsh mean that you will often end up with different spellings for a placename which sounds identical in both languages. This has happened in both directions (Carnarvon was derived from the Welsh, Fflint from the English) and sometimes more than once (current belief is that Caerdydd came from the English Cardiff, which came from the presumed Welsh Caerdaf).
Policy for employing Cambricisations of non-Welsh place names in the world is anything but fixed: see
this page for a listing of what three bodies (and Wikipedia) call the countries of the world. Sometimes the foreign name is adopted exactly, sometimes transliterated, sometimes translated.
Some placenames outside Wales (e.g. Liverpool, Manchester, Germany) have Welsh names that are commonly used today (Lerpwl, Manceinion, Yr Almaen) that were not used at all in 19th century newspapers: they'd insert the English name in italics. Others have Welsh names that date back to antiquity (London/Llundain). It should be remembered that this was at a time when all formal education was through the medium of English: the only Welsh-medium education was within the Sunday School movement, where you'd only expect to learn about the geography of places named in the Bible.
In those same Welsh newspapers, Wrexham would have been referred to as Gwrecsam: it's not a modern revision (as for example Port Madocks -> Portmadoc -> Porthmadog). Both names apparently derive from Wristlesham, the name used about 900 years ago.
Both translations and transliterations can cause consternation among locals: Transliterations of
Sully and
Varteg have suffered from pushback in South Wales, as did a literal translation of Valley on Anglesey to Y Dyffryn. In the latter case, residents preferred the transliteration Y Fali instead. (Y Farteg wasn't as well received!) The origin of the name Valley isn't universally agreed upon, but I understand it to be based on the Irish Baile/Bally when navvies were camped there building the Chester and Holyhead Railway.
See? I managed to steer the thread back toward railways in the end!