This movie is about writer who is working at a Puerto Rican newspaper in the 1960s, who also failed to reveal some information about his boss to public.
Why is the source book / movie titled "The Rum Diary"?
The novel is based on the real life incidents of the author Hunter S. Thompson.
From the Wikipedia page of the novel,
Thompson himself travelled from New York to San Juan in 1960 to write for an ill-fated sports newspaper on the island of Puerto Rico. Thompson had unsuccessfully applied to work at the larger English-language daily called The San Juan Star which novelist William J. Kennedy edited. While in Puerto Rico, Thompson befriended many of the writers at the Star, providing the context for The Rum Diary's fictional storyline.
By above paragraph, we know that it is based on his real life experience.
Now, why is this novel named The rum diary?
This is an early novel set in the 1960's but was published very much later in 1998. This was discovered by Johhny Depp from the original author Thompson's manuscripts dated from 1960's. These two were good pals. This was the reason Johhny Depp acted in Fear and Loathing in Las Vegas which is also an adaptation of Thomson's work.
The Rum Diary is an early novel by American writer Hunter S. Thompson. It was written in the early 1960s but was not published until 1998. The manuscript, begun in 1959, was discovered amongst Thompson's papers by Johnny Depp.
diary refers to the daily life experience and the incidents happened in a life of a person. In the novel, an author named Paul Kemp is the narrator. He works for a major newspaper. The main plot of the novel is describing the lives of the Americans staffed in the newspaper.
Set in the late 1950s, the novel encompasses a tangled love-story involving jealousy, treachery and violent alcoholic lust among the Americans who staff the newspaper.
Rum is used to indicate the alcoholic and violent lives of the people involved in the movie. It also represents the role of alcohol in the movie. Alcohol has a significant role in the plot of the movie and is shown many times.
The basic story and the character names from the novel are not changed for the movie but the screenplay is written and directed by the director Bruce Robinson.
The movie is set in Caribbean Island Puerto Rica.
According to this Wikipedia article, rum has importance in Puerto Rico's economy.
Rum (ron in Spanish) production has been an important part of Puerto Rico's economy since the 16th century.
Thanks to BCdotWEB for the tip.