The lion was named Akbar, after the Mughal emperor of the 16th century, and the lioness was named after the Hindu goddess Sita.
The Vishwa Hindu Parishad (VHP) objected, claiming it was sacrilegious to name the lioness after a goddess.
It also took issue with the lions remaining in the same wildlife park.
The North Bengal Wild Animals Park in the Siliguri district is currently home to the two large cats.
The court ruled on Thursday that names derived from “Hindu gods, Muslim prophets, [revered] Christian figures, Nobel laureates and freedom fighters” are not acceptable for animals.
“Bijli [lightning] is a possible name for it, or something similar. However, why use names like Sita and Akbar?” Saugata Bhattacharya, the Judge, inquired.
The court also inquired as to whether naming dogs and other pets after people would be wise. The judge remarked, “You could have avoided a controversy.”