The problem right now with non-standardized delimiters is that there is no way to distinguish the case of a “name in its own right” from there being two equally valid but different names used by different local linguistic groups. This is specifically the situation that normalizing on the semicolon separator for equally valid but different names can help distinguish. If the name really is hyphenated, don’t change the hyphen to a semicolon. If the name really isn’t hyphenated in practice but there are two different versions that are equally prominent and valid, then don’t use a hyphen, use a semicolon.
I believe that you are misunderstanding Mihn’s comments. If the single name is understood to include hyphens and other punctuation, then they should be kept. The cases where semicolon should be used is where local speakers of one language use one name and local speakers of another use a different name and those linguistic groups don’t have a unified understanding that the name should be compounded.