Adding on to what other people that say about "Fairy Tail" means "endless adventures and mysteries", I also believe Mavis also meant the name was based of on Zera.
In Fairy Tail Zero, Mavis started to form a guild at the place (Magnolia) where Zera's dad and the Red Lizards guild have all been executed. Mavis wanted to help the village to fulfill Zera's dream, by starting a new guild with a name related to her. There was a scene where Mavis pointed out about Zera's hair looking like two tails and that Zera said that fairies would always be in Mavis' heart and where did Zera go? Right back into her heart, referring Zera as the fairy with tails.
Now that you might have thought about it, Zera might actually been the fairy Mavis has always been looking for.