Take a look at the start of section 2 of the AISC manual, this describes the nomenclature quite well.
Subscript n (Rn) is the nominal capacity. Essentially the capacity with no adjustment for LRFD or ASD.
Subscript a (Ra) is the required allowable capacity for ASD. Ra ≤ Rn/Ω.
Subscript u (Ru) is the required ultimate capacity for LRFD. Ru ≤ φRn.
I can see your point, though. You would think subscript r would be used for "required". This is done somewhat, if you look at chapter H for combined forces in AISC 360 you see that Rr is the "required" strength for LRFD or ASD.
Professional Engineer (ME, NH, MA) Structural Engineer (IL)
American Concrete Industries