Donald Trump
Even though he's not the main character in the book (its writer/protagonist/narrator John Bolton is), President Donald Trump is the main focus of the book. In the book, Bolton does two things. Primarily, he makes the case that Trump ought not be President of the United States and that is stupid, idiotic, immoral, and incompetent man. To illustrate their points, Bolton recounts his experiences with Trump during his tenure as National Security Advisor - from the Nuclear Summit in North Korea to the killing of an infamous Iranian general.
John Bolton
Naturally, because John Bolton wrote The Room Where it Happened and took part in the events described therein, he is a main character in the book. Bolton also served as the National Security Advisor to President Trump for the better part of a year. Although his tenure was by many accounts rocky, Bolton brought experience to his role - even though many thought it was bad experience.
Bolton and the Trump administration was instrumental in the destruction of ISIS and the deaths of leading terrorists, for example, even though Bolton was later critical of Trump and his decision-making process.
Vladimir Putin
The President of Russia, Vladimir Putin is a significant character in the book. It was Putin's Russia, for example, that interfered in the 2016 Presidential Election in the U.S.