Two Rhaandarites were present at Starfleet Headquarters air tram station in San Francisco on stardate 7410.2. They were seen speaking to an Arcturian on the lower platform in the background when James T. Kirk and Sonak parted ways at the top of the stairs.
Two early sources indicate the species was intended to be named "Vegan". Firstly, the shooting script for The Motion Picture (dated 19 July 1978) mentioned "high-domed Vegans" as an example of the aliens present in the Starfleet Headquarters scenes.  Also, Steven Lance's character was described as "an alien being from the planet Vega" in a publicity photo.  Meanwhile, one of the call sheets for The Motion Picture (dated 7 August 1978) only described Billy Van Zandt's character as "alien ensign", while the movie's closing credits simply describe him as "alien boy". Other sources identify the species as being called "Rhaandarites".
This species was designed by Fred Phillips and Robert Fletcher for The Motion Picture and was one of numerous new species in the film that, with the approval of Gene Roddenberry, were named by Fletcher as well as provided a backstory by him. The following is a brief description, in Fletcher's own words:
"RHAANDARITES – From star system Rhaandaran. Simple, gregarious people. Women as big and strong as the men. Long-lived. Are like children, don't mature until 150 years old. Can grow to eight or nine feet with full height when about 200 years old. Crew member on Enterprise bridge, played by Billy Van Zandt, is young, about eighty-five. Extremely faithful, good at carrying out commands, not at giving them. Little visual sexual difference. Women designated by a spot on forehead of aluminum and black resin. Costume: silver and black lamé. Necklace: used for communication. All-purpose jewelry with machinery built in, of resin, dark gray plastic. Toy parts used for machinery that can be seen inside jewelry." (The Making of Star Trek: The Motion Picture, p. 132)
Word-for-word portions presented in Fletcher's initial description above were later excised in an article appearing in the January 2002 edition of Star Trek: The Magazine Volume 2, Issue 9, entitled "Who is that Alien?".
In an interview with Robert Fletcher – published in the February 1980 edition of Fantastic Films, as part one of a two-part interview with him, called "The Star Trek Costumes" – a paragraph about this species recalled much of his original description, with a bit of new information:
"From the star system Rhaandaran comes another race similar to Earthlings in their general appearance. They are a simple, gregarious people who carry the unisex look to its ultimate. Everyone dresses alike regardless of sex or age, both of which is difficult to ascertain without a scorecard. Rhaadarites [sic] are considered children until the age of 150 and don't even reach their full height – 8 or 9 feet – until they are at least 200 years old. Both female and male Rhaadarites [sic] are of equal physical strength and size and the only way to determine a lady Rhaadarite [sic] from her brother is by her jewelry. In the center of the female's forehead is a small black and silver disc which she wears at all times. The Rhaadarites [sic] are generally considered the country bumpkins of outer space and prefer not to leave their home world which accounts for the fact that only one 85-year-old Rhaadarite [sic] youngster is found in the Enterprise crew." 
In an interview appearing in the March 1980 edition of Fantastic Films, part two of "The Star Trek Costumes", Fletcher revealed more information about these aliens, who were now called "Rhaandarites", and the design of their costumes:
"These are the Rhaandarites. The lady is on the right; remember that the jewelry denotes the sex. This material is a black and silver lame, a very sensuous, clinging, sex material and these two guys are very big men. I thought it might be fun to dress them in this particular material. The necklace serves two purposes, first it is a lovely piece of jewelry, and second, it can be used for communication – an all-purpose jewelry with machinery built in. The necklace is made of a poured resin and a dark grey plastic. If you got very close to this piece you could look inside and see the tiny toy parts that were placed inside to simulate a working apparatus."
"Ve's biggest project each day involved making up Billy Van Zandt, the Rhaandarite alien on the bridge. This prosthetic makeup (makeup which involves appliances which must be attached to the actor's face or head) included an oversized brain structure, covered with Billy's own hair, followed by a lacy gray hairpiece wig to make him look eighty-five years young. The whole process took anywhere from forty-five minutes to a full hour. His character also called for him to wear contact lenses, which had black centers surrounded by yellow and orange. These made it virtually impossible for him to see, and most of Billy's scenes were done by touch alone. The enlarged brain appearance of this alien creature earned it the name of 'Bumphead,' and for a long time before the invention of a true generic name, Billy Bumphead became quite well known around the lot. Of course, there were exceptions, as when visitors to the studio, unaware of the excellent makeup job, wondered about the poor fellow with the malformed cranium who probably didn't have long to live!"
According to Star Trek: Star Charts ("United Federation of Planets I") and Stellar Cartography: The Starfleet Reference Library ("Federation Historical Highlights, 2161-2385"), there was a planet named Rhaandar in the star system Rhaandar (Alpha Indi), which might possibly be the system of origin for this species, in the Beta Quadrant. This system's primary was a F-class star. In 2378, Rhaandar was listed as a Federation member.
In non-canon, the Rhaandarite species and the unnamed crewman from The Motion Picture were given a much fuller treatment in Christopher L. Bennett's novel Ex Machina. Further, the planet Rhaandar was mentioned offhand by Federation politicians in the Star Trek: Destiny novel "Lost Souls".