Take a look at the start of section 2 of the AISC manual, this describes the nomenclature quite well.
Subscript n (R[sub]n[/sub]) is the nominal capacity. Essentially the capacity with no adjustment for LRFD or ASD.
Subscript a (R[sub]a[/sub]) is the required allowable capacity for ASD. R[sub]a[/sub] ≤ R[sub]n[/sub]/Ω.
Subscript u (R[sub]u[/sub]) is the required ultimate capacity for LRFD. R[sub]u[/sub] ≤ φR[sub]n[/sub].
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 R[sub]r[/sub] is the "required" strength for LRFD or ASD.
Professional Engineer (ME, NH, MA) Structural Engineer (IL)
American Concrete Industries