I won't presume to know the filmmakers motivations regarding the film's title, but it is a poor and provocative choice since the film's main character is an Italian-American from the Bronx.
For those who don't know, the Green Book was a motorist's guide for African Americans traveling through the American South during the era of Jim Crowe laws. And if you don't see why the film using it as a title is an issue, you might want to start paying more attention.
The real shame is that the story of the friendship between Tony "Lip" Vallelonga (Viggo Mortensen) and Dr. Don Shirley (Mahershala Ali) is one worth telling. Their story is true, and frankly unbelievable. The two met when Dr. Shirley, a classical pianist, hired Lip as a chauffeur/bodyguard for his 1962 tour through the south.
Both Mortensen and Ali give award-worthy performances. Their chemistry is what makes the film works. However, the film relies on some seriously tone-deaf tropes mostly because the film is very clearly told from Lip's perspective. Seeing as the script is written by Vallalonga's son, that's hardly surprising.
The script goes a little too easy on Lip, who certainly comes to recognize the struggle that Dr. Shirley faces but doesn't seem to truly change. At times the film even seems to suggest that Dr. Shirley benefited more from their odd-couple relationship, which is truly cringe-worthy.
In the end, it's not a bad film, but it could have been truly great had it broadened its scope and remembered that there were two sides to this story.
...just for fun: