Desmond Miles is the Animus user who relives Ezio Auditore's memories in Assassin's Creed II.
Desmond enters the Animus, a fictional machine that reads genetic memories, so the modern-day Assassins can study Ezio's life in Renaissance Italy. Ezio is Desmond's ancestor, which gives the machine access to those inherited memories.
The framing story alternates between Desmond's modern-day escape and Ezio's historical experiences. Desmond is not playing Ezio in the ordinary sense; he is experiencing a reconstructed ancestral past while remaining connected to the contemporary Assassin conflict.
Several other characters use or operate Animus technology across the series. Clay Kaczmarek is another important subject, while William Miles is Desmond's father. Those names are common mix-ups, but neither is the central Animus participant in Assassin's Creed II.