English likely got the name from Portuguese, “Japão” *[ʒä’pɐ̃ŋ] (see note). I don’t think that it’s from Dutch “Japan” because otherwise the name would end as “Yapan”, as Dutch uses a clear [j] (“y”) sound.

In turn Portuguese got it from either Malay or some Chinese language. I think that it’s from Cantonese 日本 jat⁶ bun² [jɐt˨ puːn˧˥]. Portuguese has this historical tendency to transform [j] into [ʒ] (the “g” in “genre”), and to mess with any sort of nasal ending.

The name in Chinese languages can be analysed as meaning simply “Sun origin”. Because it’s to the east of China.

In turn, there are a few ways to refer to Japan in Japanese:

• 日本 / Nihon - it’s a cognate of that Cantonese jat⁶ bun². Except that it uses the Japanese rendering of Wu Chinese words.
• 日本 / Nippon - same as above, with a slightly more conservative pronunciation (Japanese converted a lot of [p] into [h]).
• 大和 / Yamato - it’s metaphorically referring to the whole (Japan) by one of its part (the Yamato province, modern Nara).
• 日の本の国 / Hinomoto-no-Kuni - poetic and dated name. 日/hi = Sun, 本/moto = origin, 国/kuni = land, の = an adposition**. So it also means “land of the origin of the Sun”. The big difference here is that all words used are inherited from Old Japanese, so there’s no Chinese borrowing involved.

*note: that [ŋ] is reconstructed for around 1500 or so (Nanban trade times), given the word was also spelled Japam back then. A more typical contemporary pronunciation would be more like [ʒä’pɜ̃ʊ̯].

**the best way I know to explain Japanese の/no is that it works like a reversed English “of”: in English you’d say “origin of Sun”, in Japanese you’d say “Sun no origin” (hi no moto = 日の本). I only remember this because of Boku no Hero Academia, because “boku no” = “of I” (my).