It doesn't rhyme with Josie in all accents - in mine Josie is JO-see, whereas Posy is PO-zee. I know that some people say the 's' in Josie as more of a /z/ than an /s/, which would make them rhyme.
https://nanowrimo.org/participants/christine-seaforth-finch
http://christineseaforthfinch.blogspot.com/