Picking different katakana for a common western name

My son's name is Robin. This is generally written in katakana as ロビン (such as "Robin Williams" 「ロビン・ウィリアムズ」 or "Robin Hood" 「ロビン・フッド). The katakana spelling makes sense because it maps to RO-BI-N, but the pronunciation is wrong. ロビン being pronounced like ROW-BEE-N. A closer pronunciation to the way we say the name in my country would be ラベン (RABEN, RAH-BEH-N)

I realize the rules to katakana are sometimes very strict and are sometimes totally loose. It seems silly to me to pick a katakana name that is pronounced wrong just because it maps more closely to western letters, but it also feels weird to "change" what is already an established spelling of a name.

I guess what I'm asking is what would you do? How did you decide to write your name in katakana especially if it's a more common name that has a situation like this, where the katakana doesn't really match the pronunciation.

Thanks!