Does "Romanization" remain the same irrespective of national pronunciation differences i.e. British English and American English? How about regional pronunciation differences within Korea? (Not certain there are any but I think I have heard some native speakers say things differently.)
Bearing in mind I consider myself an intermediate/lower-advanced speaker and not fluent (although to anyone that doesn't speak Korean I sound it, I can have a conversation using only Korean with native speakers, but some of it is me not remembering a word so having to explain what the word I'm looking for is, but in Korean).
So it does remaining the same regardless of national pronunciation differences, however, they actually use American English as their standard form of English pronunciation. There are a number of words in Korean where they use the English word pronounced in a Korean way (called Konglish), and generally they use the American pronunciation as a base.
There are regional differences (사투리, satoori), but to my understanding this isn't that they generally pronounce a given word differently (i.e. same Hangul, different sound), but they use an entirely different word or ending, and use the correct Hangul for that pronunciation. For example, Tofu in standard Korean is 두부 (Dooboo), but in the Busan region, they call it 조포 (Jopo). They would write it as Jopo, not Dooboo and pronounce it as Jopo. So if they change the sound for the regional variation, they change the writing to match it. Does that make sense?
Even with any regional variations though, the Hangul-to-sound is consistent. The Hangul alphabet was invented to have lots of references to the position of the lips, tongue and throat when making that sound. For example:
One of the best pieces of advice I received when learning Korean was to forget trying to write it out using English letters. Any of the available romanisation systems is at best an approximation of the sound in letters where your brain will already have a concept of what that letter sounds like. So I was told "forget English letters, learn Hangul and how each letter sounds and pronounce them that way". One good example of that is ㄹ which is "either L or R". This sounds confusing but it's actually a sound somewhere in between that we don't really have in English, and it sounds slightly different naturally depending on what sound is before/after it. But when we think "L or R" we never get quite the right sound to come out of our mouths, and we confuse ourselves on which sound to use in a given situation.
In the example we were discussing, 도복 Dobok has two ㅗ letters (written out bit by bit it's ㄷㅗ ㅂㅗㄱ) which is "oh" so whether you pronounce that sounds (incorrectly) as an "ah" instead of an "oh", either way it should be the same letter. For example, I could understand Dabak or Dobok (although officially only the latter is correct), but to use Dobak feels weird (like the two syllables SHOULD have different vowel sounds, and they most definitely should not).
I hope some of this makes sense, it's something that's become quite natural to me since I started learning Korean (properly) in 2014, so explaining it in English is not something I have to do very often. Also, as I said at the start, I'm not fluent/native, so open to being corrected/educated by anyone fluent/native.