I figured it out by ear in several songs, looks like a dim chord but with a slightly higher last note but cannot put a name on it.
I'm calling it "dim+" for my personal notes, but I'd like to know the official name.
This is a C half diminished 7 chord:
The scale that typically pairs with this half diminished chord is the locrian scale. For example, C half diminished 7 (usually notated C min 7 ♭5 or Cø7) would be played with the C locrian scale:
The locrian mode is the seventh mode of the major scale, and thus C locrian has all the same notes as the D♭ major scale, as can be seen above. There are other scales that work with half diminished chord, but the locrian scale is a good start. C half diminished can resolve to D♭ maj, or it can be part of a "minor ii-V-i progression," such as Cø7 - F7♯9 - B♭ minor. There are other functions for this chord, but these are two big ones.
That would likely be D♯m6, third inversion, with the notes as you've written them.
Or, if the tonic here is definitely C, it would be C1/2dim7, but the notes would be C E♭ G♭ B♭. Also known as the Tristan chord.
It's a C half diminished 7th chord. I often spell it as C-E♭-G♭-B♭, but your spelling at least gets the notes right.
In jazz chord/scale theory, this chord is a C half-diminished chord, and is the sixth mode of E♭ jazz minor (melodic minor ascending and descending), the scale itself being called the half-diminished scale.
It is C #6sus#2#4no5
I identify chords with my brain