Fusō

They were citizens of Amegakure and lived in a small village with their son Nagato.

Background
During the Second Shinobi World War, Nagato and his parents were hiding in their battle-damaged house when Konoha ninja broke in looking for food. Nagato and his parents tried to sneak away but when they were detected, his mother and father fought the ninja to give Nagato a chance to escape. The Konoha ninja, assuming the couple were enemy ninja, attacked and quickly killed Nagato's parents.

Witnessing this, Nagato unknowingly awakened his Rinnegan, and he subsequently killed the two Konoha-nin. Nagato buried his parents before leaving to search for food. The death of his parents is the first great tragedy of his life, and in his eyes evidence that the peace Konoha preaches comes at the cost of others' lives.

Trivia

 * Based on Obito's words, at least one of them is descended from the Uzumaki clan. A common trait of the clan is red hair. While it is unknown if either of Nagato's parents has red hair in the manga, in the anime, his mother's hair is red.