Since there is no way to confirm this kind of information, people seem to just create "days" for Touhou characters. I'm in a discord server that has a bot that anounces when each character's day is, it is usually based on the character's name and japanese numbers e.g. 10/9 (Month/Day) is Akyuu's Day because A is 10 in hex and nine in japanese is "kyuu" (九, きゅう). But there are other ones that are really unique, like Rumia's, which is 10/7 because the kanji for ten is 十, which reminds of her T-pose and one of the readings is "so". 7 is "nana" (七, なな). If you split nana in half and put it after "so" it becomes "so na" which is the start of her phrase "sou nano ka?" (is that so?).
