How should hyphenated Chinese and Korean names be capitalised?

When Chinese and Korean (and, rarely, Japanese) names are written in Roman characters with hyphens between syllables, should the syllable after the hyphen start with a lower-case letter or an upper-case letter?

In the “Eastern Name formatting” instructions, “Yun-Fat” is written with a hyphen between the syllables and the second syllable starting with an upper-case letter.

But, in the same example, “Mu Bai” is written with a space between the syllables instead of a hyphen.

Anyway, the instructions don’t specifically mention capitalisation, nor whether to use hyphens or spaces; they are only about the order to put names in. So I’m not sure I should use the example given to clarify one point as guidance for a different point.

Meanwhile, some other Chinese and most Korean names of both real people and characters I’ve come across are written with the second syllable starting with a lower-case letter, such as “Maggie Ho-yee Cheung”, “Yeung Wai-lun”, “Song Kang-ho”, “Bong-soon” etc.

Personally, I think using a hyphen and a lower-case letter after it is the least confusing option, as these are not exactly the same thing as Western double-barreled names, like “Mary-Jane”, in that they’re not always made up of two separate names that could each be used on its own.

Capitalising the second syllable or putting a space between the syllables is arguably more like writing Jonny as “Jon-Ny” or “Jon Ny” (though not quite the same, as some syllables used in Chinese names can be names on their own, and in Korean names the first syllable is traditionally a generational marker shared between cousins or just siblings).

But I also like to have consistency, so I will go with whatever the rule is.

The general rule of formatting names according to how they mostly appear in on-screen credits isn’t much help with Chinese and Korean names because, unless someone does a lot of work in countries that use Roman characters, their name mostly appears in on-screen credits in Chinese or Korean characters.

And when someone’s name is written in Roman characters on official posters, trailers, video packaging, press notes etc., these often format the names all in capital letters. When they don’t, they still tend to format all the names consistently (i.e., all with spaces between syllables, all with hyphens and lower-case letters after the hyphens, or all with hyphens and upper-case letters after the hyphens).

So neither is much use for indicating a particular person’s preference for how their name should be capitalised. That’s why it would be helpful to have defaults to fall back on (as several other user-contributed sites do).