Nekomiya Mana's family name, 猫宮 Nekomiya, is translated as "cat shrine," whilst in her given name 又奈 Mana, 又 Ma means "again" and 奈 na means fruit tree.
It can be assumed that her name and surname were chosen so that the first kanji of each would form the Japanese word 猫又 nekomata.
Nekomiya Mana's nickname is a reference the mythical Japanese creature 猫又 nekomata, a 妖怪 yōkai that can take the shape of a cat with two tails.