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Your first and middle names contain vowel sounds that are difficult, if not impossible, to represent in Arabic. There are no letters or diacritical signs that precisely capture the sound E in “Emily” or the diphthong AY in “Ray,” so representing these sounds is an approximation at best.
For “Emily,” I would suggest إمِلي, but I thought that you should know that the famous writer Emily Nasrallah spells her name إميلي.
For “Rae,” my first suggestion is رَي
My second suggestion is راي
I am assuming that “Rae” is pronounced like “ray.”