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.
As of 3-7-21 when I last updated this page, Plants of the World Online lists 601 genera in this family. The Wikipedia article is very informative, but the numbers are not up-to-date.