It would be written as "レイチル" (Rei-cheru).
Rachael = Raquel
バン is the katakana spelling.
The word katakana means "fragmentary kana" or "fragmented kana". Source: Wikipedia, Japanese to English Dictionary.
The word "anime" is written in katakana like, アニメ. The reason for this being that it is actually a shortened version of the English based word, "animation" which is written in katakana as アニメショーン (animeshoon).
Katakana: ヘザーRomaji: Hezaa
Rachael is not an Irish word so it has no meaning in that language.
katakana script, beddo
So-Se-Ji in katakana and in hiragana with these symbols.
Kanji/Katakana: クリ ストファ Romaji: Kurisutofa
It is Japanese, more specifically katakana. Katakana is used for loan words taken from other languages. The words in katakana are typically pronounced very similarly (within the confines of the Japanese language) to the original word. In roomaji (that is, the Japanese word but written in roman letters) this particular word is pankēki (pronounced like pan-kay-kee). This word is "pancake"... if you say pankēki out loud, you'll hear the similarity to the English word.
"Saint Bride" in Japanese katakana is written as セント・ブライド. The word "Saint" is represented by セント (sento), and "Bride" is represented by ブライド (buraido). Katakana is typically used for foreign names and loanwords in Japanese.
The Japanese word for 'Jamie' is typically written in katakana as ジェイミー (Jeimī). Katakana is the writing system used in Japanese for foreign names and words. Since 'Jamie' is a name, it is transliterated rather than translated.