The Logo -- played by actor Jason Clarke -- is portrayed as a raging alcoholic in the series ... and while a warning explicitly says the show is a dramatization of real events, West says it has caused serious anguish to his family, according to ESPN.

In fact -- West's so pissed about the show ... his attorney, Skip Miller, fired off a letter to HBO and producer Adam McKay accusing the show of acting with malice ... and claiming the warning does not protect the project from liability.

"Jerry West was an integral part of the Lakers and NBA's success," the letter read, according to ESPN.

"It is a travesty that HBO has knowingly demeaned him for shock value and the pursuit of ratings. As an act of common decency, HBO and the producers owe Jerry a public apology and at the very least should retract their baseless and defamatory portrayal of him."

The show is based off Jeff Pearlman's book, "Showtime: Magic, Kareem, Riley, and the Los Angeles Lakers Dynasty of the 1980s" ... but West's team says his scenes in the show did not appear in the book -- nor did they happen in real life.

Many members of the Lakers org. also backed West -- including Kareem Abdul-Jabbar, Mitch Kupchak and Michael Cooper ... who claim the fits of rage and binge drinking were entirely fabricated.

Quincy Isaiah -- who plays Magic Johnson -- defended the show to TMZ Sports recently ... saying it's meant to be entertainment and they meant no disrespect to the real people portrayed in the show.

Clarke previously raved about his experience on the show ... applauding producers and directors for giving actors the freedom to be as expressive as they'd like.

As for the real West, he's been hailed as a true professional and basketball genius ... even receiving the Presidential Medal of Freedom from Donald Trump in 2019.