I've noticed that when it comes to naming, Hookpad doesn't distinguish between certain sus4 chords that may have different notes due to the chord's position in the scale. For example, when in F major a I sus4 chord is named "F sus4", but in C major a IV sus4 chord is also named "F sus4", even though these two chords have different notes (F-Bflat-C vs F-B-C). Shouldn't the second chord be named as "F sus(#4)" or something similar?
You're right, this is a problem with our chord naming framework. Same with viiºsus2 which in the key of C should be something like bºsus♭2. In the next version of Hookpad, quality will be determined on each chord from scratch and so these chords will be named correctly.