In an article appearing in the January 2002 edition of Star Trek: The Magazine Volume 2, Issue 9, entitled "Who is that Alien?", the following information about the Rhaandarites, as taken from Fletcher's original background notes, added:
"The Rhaandarites were a simple, gregarious people who were much better at taking orders than giving them. They were very long-lived and didn't really reach maturity until they were 150 or so. Unfortunately, the Rhaandarite on the Enterprise bridge was only supposed to be 85 years old."
The script for The Motion Picture mentions "high-domed Vegans" as an example of what aliens are present at the Starfleet Headquarters scenes.  Steven Lance's character was described as a Vegan in publicity material. 
"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."
According to backstage info, the name of the Rhaandarite homeworld is Rhaandaran.
Rhaandar (Alpha Indi) was the name of a star in the Beta Quadrant. The primary was a Class F star. Magnitude of this star was +3, which was 10 times brighter than Sol. Rhaandar was the name of a planet in the system. too, and had, by 2378, become a member of the Federation. (Star Trek: Star Charts, United Federation of Planets I)
In non-canon, the Rhaandarite species and the unnammed crewman from ST:TMP are given a much fuller treatment in the book by Christopher L. Bennett Ex Machina. Further, the planet Rhaandar is mentioned offhand by Federation politicians in Star Trek: Destiny "Lost Souls".