Question: as Kobayashi is his family name, should this be Issa Kobayashi? Japanese typically list last name then first name, but Goodreads usually does it the Western way (which is why it's Haruki Murakami and not Murakami Haruki). Do we have a rule for this?
Well, he is known to Western readers as Kobayashi Issa (or just Issa). As regards Japanese authors, I have the impression contemporary authors tend to be written in the Western way and less recent authors tend to be written in the Japanese way.
These profiles are for the same author:
Kobayashi Issa
Issa Kobayashi
Kobajaši Issa
Cheers!