No, it’s called Yuri on Ice because the characters’ names are Yuri (and it was also chosen to allude to gay romance, despite it being between men instead of women). This is a play on words by instead referring to the type of Yuri featuring sapphic romance, as opposed to the name. “Yaoi on Ice” would only make sense if someone’s name was Yaoi, though that isn’t a traditional given name, unlike the name Yuri.