Romulus Augustus was the teenage son of a warlord who had taken over Rome. The eastern empire did not recognize his successor state as Rome, and did not recognize any Emporer after Julius Nepos.
The warlord gave Romulus Augustus that name in an attempt to legitimize his claim to the throne.
It didn't work. He was overthrown rather quickly. While the warlord was killed, Romulus Augustus himself was considered so irrelevant that they let him live.