Luna means moon in the sentence Luna Park as well.
That's what I've found about this attraction:
Luna Park comes from “A Trip to the Moon”, a park built by Frederic Thompson and Elmer "Skip" Dundy. They were best remembered for building Coney Island's Luna Park in 1903 and Manhattan's famous Hippodrome Theater in 1905.
If there was one attraction not to be missed, it was Frederick Thompson's A Trip to the Moon. Possibly 1 out of every 20 people who came to the Pan-Am took a trip to the Moon. Unlike other Midway attractions, "passengers" were active participants in their trip, not merely observers. Admission was 50¢, double the cost of many other attractions, but it was worth the price. The Airship Luna departed every half-hour for a trip to the Moon with 30 passengers on board. The Luna was a cigar shaped craft that sported a large pair of red, bat-like wings. Passengers were seated in deck chairs, and with the sound of a rattling anchor chain, the Luna began her ascent. To one side, the passengers could clearly see the Electric Tower and the Pan-Am grounds and soon they grew smaller as the Earth seemed to fade from sight. The ascent was so real that some passengers experienced fainting spells. Robert Grant reported in Cosmopolitan that an elderly lady next to him could not be convinced that the spaceship was in fact still on the ground. Luna passed through an electrical storm, but passenger were told not to worry for they were safe in the hands of a veteran pilot who had made the lunar trip many times.
Upon arriving on the Moon, visitors found a world of giants and midgets. The diminutive, moon-dwelling "selenites" guided the visitors through the underground wonders of the Moon. They passed through a bazaar and were even offered pieces of green cheese. Finally, they arrived at the Castle of the Man in the Moon, which was guarded by "giants". There in a great hall, seats were arranged for the guest from Earth. The Man in the Moon, bedecked in ermine robes studded with jewels, sat in a mother-of-pearl throne. In the middle of the great hall was the Geisler Electric fountain, which was colorfully illuminated. Emerging from behind the fountain, the Moon Maidens danced to entertain the guests. However, there was no return trip on the Luna, rather guests were ushered out a side door that led back to the Midway. There were many famous travelers to the Moon in 1901. Senator Chauncey Depew, Secretary of War Elihu Root, Secretary of State John Hay, General Nelson Miles who captured Geronimo and Thomas Edison all went to the Moon, and it is very likely that President McKinley took a trip to the Moon the day before he was shot in the Temple of Music. The voyages did not end with the closing of the Pan-Am. Thompson moved A Trip to the Moon to Tilyous's Steeplechase Park on Coney Island where the Luna continued to enthrall passengers on a lunar odyssey.
A legend tells that Luna was the name of Dandy's sister but in reality, Luna actually comes from the Latin translation of the English word "moon".