GRX
GRX, unlike Shimano's other model names, identifies a family of groupsets. That is, GRX is available in 3 spec levels equivalent to Tiagra, 105, and Ultegra. GRX was the first groupset to be specifically designed and/or marketed as a gravel group, and it was released in mid 2019.
In mid 2018, Shimano released a niche component, the Ultegra RX800 clutch rear derailleur. My recollection is that at the time, no road double group had a clutch rear derailleur, although SRAM included clutches on its Red and Force AXS road rear derailleurs released in mid 2019, and SRAM appears to have had clutches on the Force HRD 1x road group that was active in 2018. Shimano intended the RX800 to be used on terrain like Paris Roubaix, which was where the RX800 rear derailleur made its debut.
Starting in 2016 with Dura Ace R9100, Shimano's official branding prefixed the model numbers for its top 3 road groups with R. I can't find anything on the history of the RX800 designation, but they hadn't used Xs in any road group for many years (the last example I know of being the 600 AX road groupset released in 1981). Xs are common in the model names for their MTB components, e.g. XT, XTR, LX. X does seem to evoke notions of going off tarmac roads, so I speculate this was their intention with the RX800 designation.
Again, I don't recall and haven't found anyone asking Shimano about the history of the GRX name. However, it seems reasonable to speculate that G is for gravel, and it may have seemed like a logical prefix to append to "RX". Shimano appears not to have chosen to give brand names to each of the groups under the GRX umbrella, and they currently refer to each group by its numeric designator. For example, GRX 800 or 810 would typically be understood as the GRX group equivalent to Ultegra (and to be pedantic, the numeric designator for the 800-level GRX cranks and some other components is 810, whereas it's 600 for the 600-level cranks; there are further variations to designate Di2/mechanical shifting or 1x/2x components).
Road Groups
For reference, the current Wikipedia page for Shimano has a table of historical models for each road and MTB group or its equivalent if available. I am not 100% sure about this, but earlier versions of the Ultegra groups introduced before 1998 (when the 7-speed Ultegra groups were launched) may just have been branded as '600'.
This answer by @RoboKaren describes how the brand names for Dura Ace, Ultegra, and 105 originated, although it was Google Translated from the original Japanese on a forum, and we don't necessarily know how reliable the provenance of the forum post is. Quoting her translation:
Finally, I will introduce my knowledge about the origin of each grade name [in the Shimano series]. The name of Dura Ace which was born in 1971 is a combination of Duralumin of the material and Durability meaning durability combined with "Ace" which wish of the world's best component. The birth of Ultegra in 1976 is a component that means Ultimate + Integrate. Concerning 105 which was born in 1982, it inherited the model number of the double lever SL-A 105 at that time and now it has become the grade name of 105.
