In Assassin's Creed Origins, the ancient Egyptian city home to the Library of Alexandria is Alexandria.
Origins is set in Ptolemaic Egypt during the first century BCE and follows Bayek of Siwa. Alexandria is one of the game's major urban areas, representing a cosmopolitan center shaped by Egyptian, Greek, and other cultural influences. Its landmarks include the Great Library and the Pharos lighthouse.
The game uses these locations as part of its historical-fiction world rather than presenting every detail as documentary history. The Library of Alexandria was a famous center of learning, but historians debate many details about its buildings, collections, and destruction. The game therefore dramatizes a well-known institution within its story.
Memphis and Siwa are also important locations in Origins. Memphis is another major Egyptian city, while Siwa is Bayek's home region. Neither is the city associated with the famous library in the question.