I am learning chord notation and I noticed that the Wikipedia page does not mention any specific notation for a chord where the root is omitted.
Omitting the root note seems to be quite commonplace, and the result sounds different than if the root note were to be included, so I assume that there should be some name or notation for this.
These are called rootless voicings, but there is no common symbol for them.
Chord symbols themselves indicate a overall harmony, and the voicing is up to the performer. In that context, the performer might choose a rootless voicing.
There are some standards for indicating voicings within a chord symbol, such as slash notation, but there isn't a standard for leaving out the root. Writing, for example, "G7(no root)" is as good as anything else.
If you were working with one or two melodic instruments, you might get into a situation where there was an implied root note for the chord, but then the decision about the underlying harmony would also be a bit subjective.
Regular old chords stack notes a third apart. If a chord has 4 notes that can be stacked into thirds, such as C-E-G-B, it would be strange to call that chord a9 (no root) when it looks so much like a Cmaj7. Similarly, if you have a situation where you can stack just 3 thirds (a triad) such as C-E-G, you could call it a7 (no root), but why? Omitting the fifths or thirds in a chord significantly changes the way it sounds, but omitting a root is such a significant change, it'd be hard to justify not just calling the chord whatever the "lowest" note in the stack is.
In the question you linked, the first and accepted answer advocated not choosing a chord with omitted root, the second answer advocates that if you want a particular sound, write out the notes and don't leave it up for interpretation, and the third points out that the root may be in the melody line on another instrument. I don't think there's a compelling reason to build a notation for chords omitting their roots because the same notes can be specified by choosing the chord a third (or fifth) up. If a conductor is confused by seeing Cmaj7 in the piano line and a9 at the top of their score, that's their problem. While there's an argument that the function of these chords defines them more than their composition, we are long past the days when music had to make functional sense, and I, as a player, would find an instruction like (no root) to be obtuse.
You can write 'G7(omit root)' or 'G7(no root)' if you like. Yes, 'Bdim' would convey the same information.
I suppose, for purposes of harmonic analysis, it might be useful to write 'G7(b9)(no root)' instead of 'Bdim7', when it IS acting as the dominant of C. But it won't help anyone play it, and chord symbols are really designed as a shortcut notation rather than for analysis.
