Having them in the English order at all times would make it unambiguous what's the first or surname, but it wouldn't honour originally Japanese names, in my opinion.
The solution might be similar to my other question on anime / manga titles, with tag synonyms.
It's a bit of a hit-or-miss for me.
I only ever watch Anime in Japanese now, so hearing/reading the Eastern order is pretty natural to me. It throws me off every now and then to hear/read it in the Western order, but a context in which it makes sense are Anglicized characters, such as Sarah MacDougal from Love Hina, or Gene Starwind from Outlaw Star.
I feel that we should be willing to accept both forms, since not everyone knows/hears the Eastern order of names, and there are series in which the names are read in their localized order.
I think it depends on which name you use. Use the conventions of the culture that the name is from, but respect the intent of the original work.
So if an English name is used in a Japanese series, then use the English name, as the creators of the series intended for the name to be represented in that way.
We should use the English ordering as the primary tag, and the Japanese ordering name as a synonym. See my answer here, which covers my thoughts on anime/manga series tags, but also applies here.
