After the death of Emperor Nero, the people of Rome were angry with the position of Emperor. Nero’s successor wanted to make people happier about his role as emperor. Thus in AD79 he commissioned the world’s largest and most impressive amphitheatre. His name was Vespasian.
Thus when the people of Rome attended spectaces to see gladiators and wild animals fighting, they had Emperor Vespasian to thank. However, they didn’t call this the Vespasian amphitheatre, they called it the Flavian Amphitheatre, because Vespasian’s family name was Flavius.