Hi, Alyssa. You are right. アリッサwould be more common than アリサ, in my view. Isaac would be ‘アイザック’. Foreign names are normally written in katakana. If written in hiragana ‘ありっさ’, it is very likely to be mistaken with something else. In katakana, it is simple and customary, whoever you ask. if you want to know the Kanji version, there is a site of the list of options. http://www.jun-gifts.com/personalizedgifts/namelisttwo/namelisttwomain.htm Yet, some of them do not look good or cool to Japanese eyes, so make sure before you choose. as for ‘ア’ and ‘サ’, you have no choice but ‘亜’ and ‘沙’ respectively. In terms of middle one, or ‘リ’, there are too many. If you're interested, please let me know.

As kanya-san said, Foreign names are normally written in katakana. It is simple and customary for foreign names. That's true, but I think It's OK to use hiragana for your name. Because you are finding your *Japanese* name. If your name was written as ありっさ’ which is hiragana of 'アリッサ', I would feel the name is kind of strange. The reason is not because It's written in hiragana but I have never heard of it as Japanese name. On the other hand, If your name was written as ’ありさ’ which is hiragana of 'アリサ', I would feel it's a natural and common name for Japanese. so 'ありさ' can be one of the candidates for your Japanese name.