Where did "Chinchew" come from? There is this Chinese city called 泉州. Mandarin: Quánzhōu. Cantonese: Cyun4-zau1. Hakka: Chhièn-chû. Min Nan: Chôan-chiu. Pronunciations found here. Wikipedia adds a local Hokkien: Chôan-chiu. Here I get Teochew: Zuan5-ziu1. Couldn't find Min Dong or Gan or other dialects, but those shouldn't matter. Postal romanization: Chinchew. Now, "chew" obviously renders the "chiu" of Min Nan and/or "ziu" of Teochew. But where did that "chin" come from? Is the postal romanisation a weird hybrid of a misheard Cantonese "cyun" (misheard as *cin and spelled chin consequently) and a correctly heard Min Nan / Teochew "ciu"/"ziu" or is there more to this?
泉州，簡稱泉或鯉，又稱刺桐城、清源、溫陵。
Although 清 can be transliterated as chin, it does not seem to be the reason.

Quanzhou, formerly known as Chinchew.
The Postal Map name of the city was (note: should be "is") "Chinchew", a variant of Chincheo, the Portuguese and Spanish transcription of Chiāng-chiu.
It is uncertain when or why British sailors first applied the name to Quanzhou. Variants include Kangiu, Chinchu, and Chincheu.

所以，Chinchew 是從葡萄牙語、西班牙語的 Chiāng-chiu 轉譯而來。