She either always was (as daughter of Styx) or became so with marriage to Hades.
Queen Persephone is the queen of the Underworld. Hades is her husband and is ruler of the Underworld.
She is the Queen of the Underworld.
Hades, who desired that Persephone become Queen of the Underworld.
No: she would need none as Queen of the Underworld and ruler of the Furies.
Hades wanted a wife and abducted Persephone.
Hades did and he trapped her in the Underworld. He forced her to marry him.
Zeus didn't become its ruler, that would be Hades
Hades took Persephone to the underworld because of Persephone's beauty.
Hades was the Greek God of the Underworld. He took Persephone (daughter of Demeter) as his wife (not by choice). So even though there technically isn't a goddess to rule the underworld, if you had to say there was one it would be Persephone.
Ruler of the Underworld, keeping the ghosts of the dead from ascending back to earth and kidnapping Persephone.
Hades needs to be respected as the ruler of the underworld. He also desires companionship, particularly with his wife Persephone. Additionally, he needs souls to fulfill his role as the god of the underworld.
Persephone is both the goddess of Spring and the Queen of the Underworld.