For example, I have this song where for an E7 I play the notes D F# G# B (all in the same octave).. would that just be called E9 even though there's no root and the F# isn't in a higher octave?
in that case it's called E9. at least where i'm from, it is understood to include the 7, whenever you use a number 7 or higher. where as if you had said 2, it is implied that there is no 7. E9 is a well known chord and it is well known to mean dominant 9 which means it includes 7 (D) and F#, and G#. it's all case by case. some chords have acheived written popularity under certain names