In Assassin's Creed III, the main modern-day playable protagonist remains Desmond Miles.
Desmond uses the Animus to relive the memories of his ancestors, including the Assassin Connor Kenway during the American Revolution. The modern-day storyline continues the conflict between the Assassin Brotherhood and the Templar Order while Desmond searches for a way to prevent a global catastrophe.
William Miles is Desmond's father and an important Assassin leader, but he is not the modern playable protagonist. Warren Vidic is a Templar scientist associated with Abstergo, and Shaun Hastings supports the team as a researcher. These characters can be confused because all are prominent in the modern sections.
Assassin's Creed III concludes Desmond's major protagonist arc in the original trilogy. Later games continue to use modern-day characters and Animus technology, but they do not make Desmond the central modern-day player character.