According to this page, the following types of characters are allowed in names:
So that's hiragana, katakana, extension, and repetition marks. Valid examples are given for each in the parentheses. Note also that many old forms of kanji are officially acceptable, but many of them cannot be displayed on computers and cannot be read easily.
The following character types are not permitted for use in names:
It says that roman characters, as well as non-standard kanji, Arabic and Roman numerals, and some other unusual characters (shapes, symbols etc. that aren't part of standard orthography) are not acceptable for registered names.
So there you have it. Assuming this source is to be trusted then we can conclude that Japanese names are registered with Japanese text only. Foreign names, as in the examples above, will need to be given at least a katakana equivalent.