Is it legal for parents to give to their child a first name with latin letters (romaji, I guess), instead of using katakana, hiragana, or kanji?
For example, if Japanese parents want to give their children the English name John, can they avoid using katakana and just use the original latin letters? Is this legal or not?
According to this page, the following types of characters are allowed in names:
名づけ（命名）に使える文字と記号
ひらがな（ゐ・ゑも含む）
カタカナ（ヰ・ヱも含む）
「ー」（音をのばすときに使う。例：リリー、サリー）
「ゝ」（一つ前の字の繰り返しのとき使う。例：なゝえ）
「ゞ」（一つ前の字に濁音を付けて繰り返しのとき使う。例：みすゞ）
「々」（（一つ前の漢字の繰り返しのとき使う。例：奈々）
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:
名づけ（命名）に使えない文字と記号
変体がな
ローマ字
アラビア文字（１・２・３…）
ローマ数字（Ⅰ・Ⅱ・Ⅲ…）
○・×・△等の図形
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.
