Why is Romulus Augustulus considered the last Western Roman emperor?

Romulus Augustulus is historically recognized as the last Western Roman emperor because his deposition in 476 CE by the German chieftain Odoacer traditionally marks the end of the Western Roman Empire.123

While he held the title from 475 to 476 CE, his reign was effectively a puppet administration controlled by his father, the Roman general Orestes. Romulus Augustulus was not recognized as a legitimate ruler by the Eastern Roman emperor, and his removal from power by Odoacer signaled the final collapse of the Western empire's political and military integrity. Following his deposition, Odoacer did not appoint a successor, instead assuming control of Italy himself while acknowledging the nominal overlordship of the Eastern emperor.412

It is important to note that while the West fell, the Eastern Roman Empire, known as the Byzantine Empire, continued to exist until 1453.1