The Oscar Wilde character is SAL o may. I would assume that he would have used an educated English (or of course Irish!) pronunciation that was prevalent at the time ... but these things can change, and the version I'm used to in South Africa is sa LO mee - usually used by speakers of Afrikaans. A European rather than an English sound.
Your boyfriend is certainly mistaken! Just as Chloe doesn't rhyme with Joe, so the -e is sounded in Salome.