How would one call a Dm with a C bass?
I was wondering as it consists of the 2nd, a suspended 4 and the 6th so should the name be C 2/6 suspended 4?
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Slash chords don't always need to be given more specific names, but if you do try to find another name for Dmin/C then the context will matter. This could be just a Dmin with a C in the bass, i.e. a Dmin7 in third inversion. This probably makes sense if the C is part of a bassline.
If it makes sense to think of this chord as having a C root for some reason, then maybe it would be fine to call it a C6(sus2), or better a C6/9(sus4).
If Dmin/C does not sound like a D minor chord, it seems like a better name would be F6, since the notes of this chord (C D F A) form an F6 in second inversion.
Dm with a C bass note will usually be written as Dm/C. It's the third inversion of D minor seventh. You state that it is Dm, so unless that's inaccurate, Dm/C (or Dm7/C as a faint possibility) is good.