Here you go noobie:

https://www.japanesewithanime.com/2017/05/quotation-marks-japanese.html?m=1

Nested Quotations

Like in English, when a quote contains a quote within, the quotation marks alternative. Typically the single quotation marks (「」) are used for the outermost quote, and the innermost has double quotation marks (『』).

Hanako wa “hai” to itta 花子は「はい」と言った Hanako said “yes.” Tarou wa “Hanako wa ‘hai’ to itta” to itta 太郎は「花子は『はい』と言った」と言った Tarou said: “Hanako said: ‘yes.’”

I wondered the same thing. After searching a little, I found these two articles (multiple since I’m unsure and so wanted to cite my sources):

https://teamjapanese.com/japanese-punctuation/#niju-kagi-kakko-二重鉤括弧-double-inverted-commas

https://www.fluentu.com/blog/japanese/japanese-punctuation/#toc_3

Both of which state that 『』are called 二重鉤括弧(にじゅうかぎかっこ) literally double hook brackets. And the normal ones 「」are called 鉤括弧(かぎかっこ) literally hook brackets.

They also state that 『』are typically used for quotes inside of other quotes.

Additionally, the Wikipedia article on Japanese typographical symbols says that they’re used for titles. (Under brackets and quotation marks, second item)

https://en.wikipedia.org/wiki/List_of_Japanese_typographic_symbols

Hope this helps! I learned a lot doing the research for it. The rest of the first two articles is really interesting to read too.