NASA named the program GEMINI after the twin stars Castor and Pollox, one of the 12 constellations of the Zodiac.
The name was suggested by Alex Nagy of NASA headquarters.
"The twins" did a good job of symbolizing the two-man crews on each flight.
Its spheres of influence include adaptability and mobility, two features the designers of the spacecraft pursued.
The Gemini missions had the following challenges to meet prior to attempting lunar missions:
Rendezvous and docking
Long duration flights
Multiple-hour work outside the spacecraft
Advanced, reliable on-board flight systems
Training of flight and ground crews.
It was during the Gemini Program that the United States caught up with and surpassed the Soviet Union in the race to the Moon.*
*From NASA "On The Shoulders of Titans, A History of Project Gemini"