I did a google of each title, and even the Rose Flower and Red Lotus brought up Janghwa Hongryeon jeon first. So go with Janghwa Hongryeon jeon, it seems to be the most common name. HOWEVER, if you wish, a lot of fairy tales in the archive are done like this:

original title | translation name (fairy-tale) or or similar. And then the characters are original name | translation name (fairy-tale's title tag)

It can get long, but it's very precise! I encourage you to do this.