The settlement that the characters are referring to is named 'Sagan', after astrophysicist Carl Sagan.
The planet featured in the film is named Epsilon Eridani B. It is a real planet in existence, and is the fifth-brightest star (by apparent magnitude) in the southern constellation of Eridanus. An orange star slightly smaller and less massive than the Sun, and relatively close to the Solar System, it is frequently featured in works of science fiction. It has been mentioned in Star Trek, Halo and Babylon 5 among others.
The name of the spaceship Tantalus II, comes from a Greek mythological figure, most famous for his eternal punishment in Tartarus. He was made to stand in a pool of water beneath a fruit tree with low branches, with the fruit ever eluding his grasp, and the water always receding before he could take a drink. It was chosen because it hints at an ordeal ahead for the survivors.
The character of Carrie Weaver gets her name from two legendary sci-fi actresses - Carrie Fisher and Sigourney Weaver.
Director and co-writer Terry Cooper stepped in to play pilot Russ Price at the last minute when the original actor became unable to complete the filming schedule after the first day of principal photography. It was too late to find and audition a replacement, so the cast asked Cooper to step in as he knew the role.