Aren't these chords ambiguous since the root isn't specified? Depending on the root, the name of the chord changes.
Ambiguity comes from various places. Part of disambiguating something is determining what sort of thing it is.
When we hear a chord with no context, we generally listen for stable intervals to determine the root of the chord, as the root is generally how we determine function.
With a C-E-G, the most stable intervals are C-G (perfect fifth) and C-E (major third).
An inversion of those notes G-E-C gives less stable intervals, but we'll often
infer a chord anyway. If we can "find" an arrangement that gives a more stable explanation, we'll hear it as an inverted stable chord.
The lowest note interacts with the higher notes, creating tensions via waves interacting.
And some chords are unstable by nature, like the Dim7 chord. That's a stack of minor thirds (with a diminished fifth and dom7) so there's no stable interval to be found. Each one of the notes has equal claim to being the root, but the lowest note usually wins.
Jazzers often like to think of a diminished chords as a 7th chord missing the root, because we like to "understand" things using stable intervals, even if they aren't there at all.
