I think part of the problem is how you called the chord generically a "diminished" chord instead of specifically "diminished seventh" or "diminished ninth" chord. As you stack up the thirds you need to keep those extensions in mind.
But—a minor third up from the top note, Bb, is Db
This introduces the same problem. You are now talking about some kind of ninth chord. If you disregard the sharps and flats and just look at letters
C E G B D you can see it's some kind of ninth chord.
C# E G B♭ makes the first part specifically a diminished seventh chord.
Now just add on the ninth, lets use octave numbers to make the ninth clear,
C#4 D♭5. You want to call that an octave, because the notes are enharmonically equivalent to an octave, but your spelling is a diminished ninth.
C# E G B♭ D♭ is a diminished ninth chord.
Of course it is enharmonically equal to a plain diminished seventh chord, but if you want to spell it with a diminished ninth, then name it with a diminished ninth.
And is there a way of naming the notes that doesn't involve enharmonic equivalent note names, or lots of double flats?
Let's do it again but with a root of
Start with letters
C E G B D
Apply flats to make a diminished ninth chord
C E♭ G♭ B♭♭ D♭♭
The way to avoid it is either:
- don't bother with the diminished ninth, spell it a just a diminished seventh chord
C E♭ G♭ B♭♭ C
- use a different root to avoid double flats
C E♭ G♭ A C, now it is an
A diminished seventh chord.
You probably should not switch around the root to avoid double flats at the expense of clear harmonic function.
C diminished seventh should resolve to a tonic of
A diminished seventh chord should resolve to
B♭. Use the spelling that make the function clear.