What is the meaning behind naming the people of Lot by this name, and what is the evidence for that from the Quran?

The people of Lot are the inhabitants of the villages of Sodom in Jordan. Allah sent Lot, peace be upon him, to them to invite them to monotheism and to abandon the practice of engaging in sexual acts with males. When they did not respond and threatened to expel him, Allah saved him and destroyed them with various kinds of torment. They were called the people of Lot in relation to their prophet, and their story is mentioned in the Quran.