Refer to the related question What non-Roman scripts keep foreign words in Roman?
You ask which Latin alphabet languages do transliterate, and why more Latin alphabet languages don’t transliterate. I know Czech does (right, Zeibura S. Kathau), but it is indeed the case that most Latin alphabet languages don’t, and certainly any that do are Eastern European: no Western European languages do.
The following related reasons, I surmise, though this is a surmise:
- Based on the Greek experience, where foreign names started showing up in Latin alphabet a couple of decades ago: respecting the prestige of the source language(s), by keeping them in their source orthography.
- Showing off that you are an intellectual and a polyglot, and you know exactly how Hungarian or French or Danish pronounces those names, so you have no need of demeaning cribs like transliteration. Remember, after all, who the people were who needed to refer to contemporary foreign names to begin with. And remember also that politically familiar names were often assimilated popularly; Napoleon, for example.
- These two points are really the same point presented differently.
- Minimising the risk of not recovering the source spelling of the name from the transliteration, in case you need that source spelling. (Who’s Smits? Smith? Smit? Smeets?)
- Once people started doing things that way: inertia.
Oh, and OP? People do write Sean in English as Shawn. But only if it’s their own kid. 🙂
Up until the 1600s, foreign names showed up around the West in Latin. And in Latin, of course they were changed to meet both Mediaeval Latin phonetics and inflection. So this is a Modern Era thing.