The person that poses for a painter is typically called a model. They will be the subject of the portrait. Famous models for paintings include the woman from Leonardo da Vinci’s “Mona Lisa”, the fictional Dorian Gray from Oscar Wilde’s The Picture of Dorian Gray, and various kings, queens, and presidents. That list of models includes, but certainly isn’t limited to, King Henry VIII of England, Queen Elizabeth I of England, President George Washington of the United States of America, and President Abraham Lincoln of the United States of America.
The first recorded instance of someone modeling for a portrait is in Ancient Greece. Often, these models were nude, but they didn’t have much of a problem with that; the gymnasiums were often full of naked men.