I could be wrong, but FWIW I doubt Hungarians include diacritics that don’t exist in Hungarian (like ñ) when writing foreign names.
In general, if the source language has a latin alphabet, we try to stick to the original spelling in most cases, but it is not uncommon to replace non-Hungarian letters with the closest one. It's a bit more complicated in case of non-latin alphabets, especially Cyrillic due to a lot of shared history.