^I think it's also partly because they're the two most popular characters in the series, so it makes a certain amount of sense for them to be a popular ship just by virtue of people putting their favorite characters together. Still squicks me out too, though.
I don't know what the ship names are in Japanese though...damn, lol.
I can help with this!
Luckily they follow more regular rules than English ship names:
-Take the first two kana (or first kanji) of each name and put them together
-I think the order goes guy-girl for heterosexual couples and seme-uke for BL couples? Don't quote me on that
-So Rizumo is 燐出 (RinIzu), RinShi is 燐しえ (RinShie), the twincest one is either 雪燐 (YukiRin) or 燐雪 (RinYuki)...what are some other ones I've seen on Pixiv? Mephisto/Amaimon is メフィアマ, etc. With Shima, sometimes people can't decide whether to use 志摩 (Shima) or abbreviate Renzou to 廉, so you get 志摩勝 (ShimaSugu) but 廉燐 (RenRin) and so on.
Also, 腐 (fu) or 腐向け (fumuke) is the tag for "stuff a fujoshi would like" so if you see a post tagged with Rin and Yukio and that, beware. Cute sibling stuff will have their full names as separate tags, no 雪燐 or 燐雪 and no 腐.
Protip: never click on anything tagged サタ燐
no matter how much morbid curiosity you're feeling, yes it's 4 am and you think you're totally up for reading a trainwreck of a fic, no you still shouldn't do it, just go to bed, there is only regret in your future, oh my god Facets what is wrong with you you speak more than enough Japanese to know that's code for interspecies pedophilia incest rape...Back to the new chapter, did anyone else feel really bad for Yukio when Rin was talking about Shiemi? I mean, I ship RinShie more than YukiShie, but poor kid...