So... is Banana Fish finished or not?
NO, it is not finished.
Why?
The anime finished after the manga:
Anime finished: December 21, 2018
Manga finished: March 12, 1994
... But MangaUpdates contains information about the anime adaptation and indicates that it is incomplete.
Watching Order (by release date)
Here you have all the anime relations we detected ordered by release date, so you can see the reason for this status in context and also use it as watching order.
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Synopsis
Ash Lynx, a young gang leader in New York City, is drawn into a dangerous mystery surrounding the phrase "Banana Fish," which is also tied to his traumatized older brother.
While investigating this cryptic phrase, he encounters Eiji Okumura, a Japanese photographer, and his assistant. Their meeting is quickly interrupted by the mafia, led by Ash's former benefactor, Dino Golzine.
When Eiji and a friend are kidnapped, Ash must navigate the treacherous world of the mafia and street gangs to rescue them and uncover the truth behind "Banana Fish," all while battling his own complicated past.