Rubiaceae Juss. is the correct and accepted scientific name for this family of flowering plants. It was named and described as such by Antoine Laurent de Jussieu in Genera Plantarum in 1789.
So far, the only species I have come across on the farm that is in this family is Galium aparine. You know, that pain in the neck “sticky feeling” plant? Ever heard of Cleavers, Clivers, Bedstraw, Goosegrass, Catchweed, Stickyweed, Sticky Bob, Stickybud, Stickyback, Robin-Run-the-Hedge, Sticky Willy, Sticky Willow, Stickyjack, Stickeljack, Grip Grass, Sticky Grass, Bobby Buttons, and Velcro Plant? Yeah, that one! Coffee, Gardenias, and Pentas are also in the family.
Plants of the World Online lists 598 genera in the Rubiaceae Family. Wikipedia says about 13,500 species in 611 genera but their source is apparently outdated. One source they list is The Plant List which hasn’t been maintained or updated since 2013. I trust The Plant List to be the most reliable database. World Flora Online is also fairly new, but they uploaded their data from The Plant List. They are currently working on revising using Plants of the World Online for up-to-date data.