If this is Katakura Ako's idea of what "pure love" is, I worry about her lol.
Seriously though, it's an interesting one. Two women (old friends?) chasing after the other's memory through sex are finally able to fall out of love when they actually fuck each other. Well, as Saki says, prostitution is often a form of therapy. Despite the melancholy tone I do read the ending as hopeful, even for Izumi.
Fall out of love sounds kinda sad, more like “get closure”
I don't know if I'd really call it "closure" to be honest, that implies a more neat and tidy ending than I get from this oneshot. Even at the end "Miya" and "Izumi" weren't being honest with each other, not even using the other's real name, despite them both clearly understanding what was going on at that point. (Not to mention Miya/Kanade very deliberately cuts contact with Izumi completely.) To put it another way, I think they're both just beginning to move on, they still have a long way to go. As Temp says, what saves this oneshot from being completely depressing isn't either of them; it's Saki who demonstrates that a real relationship can be built on the ruins of heartbreak.
I'd say it's a little more hopeful than that. For one thing, the title is a clue, since in the most popular version of Snow White, she's cursed in enchanted slumber and awakens with a kiss. Kanade was sleepwalking through life, but after "kissing" Izumi, she's able to wake up and move on.
Also, there are hints that Saki engineered this whole thing. It seems that she realized who Izumi was and convinced her to request a threesome, I guess as a way to help Kanade. Judging by her reactions, it looks like she wasn't sure how Kanade would react and didn't know who she would end up choosing.
I don't see Kanade using her stage name as her being "dishonest", rather it seems like after that first kiss she retreated into her role as a professional as a way to deal with her emotions. She still told Izumi the truth when she asked why she became a sex worker.
I think the author is pretty clear that this is a happy ending for Kanade and Saki. They've been lovers for a while now, but it looks like they were stuck in a holding pattern, unable to move forward. Taking eachother's hands, and then quitting their jobs together is a pretty clear sign that they're now able to move on.
I do agree with you that the ending is not particularly hopeful for Izumi. She doesn't seem to take closure from the experience, and that's where the rest of the title plays in. In the Disney movie, Snow White is awakened by "true love's kiss", and marries the prince. In this version, the prince kisses Snow White, she wakes up, and then runs away with her actual lover, never to be seen again.