The chord, is a Csus2+4 combination without the perfect fifth. The inversions are Dm7 (without fifth) and F5 (with major sixth). WhatI want to know is the name of this chord?
I think you are missing the point from commentators. We don't need details about
C D F in isolation we need to know the other tones around that.
Below are three examples putting
C D F into a harmonic context. I've highlighted with two colors to make clear that the mere group of notes
C D F - which are in the red boxes - are not necessarily the proper chord. In the green boxes are the proper chords. Notice that those "proper" chords can span several rhythmic events...
The first treats
C D F so that the
C is just a neighbor note movement within a
B diminished chord. Again, notice that everything in the green box can be properly considered the
B diminished chord. Or, you could consider the chord
G7 with the root omitted. Either way the chord is root position.
The second treats
C D F as a
D minor seventh chord in third inversion moving to a
G dominant seventh chord. Here the red and greeen boxes overlap.
The third treats
C D F as a suspension within a
C chord in first inversion. In this case the green box groups
C D F with the
So... that's three different ways to identify
C D F depending on what you do with the other chords.
In order to name the chord in a harmonically meaningful way you must name it within the harmonic context.
If the green boxes seem confusing, if they look like they contain 3, 1, and 2 chords, keep in mind this is a more conceptual understanding of harmony and chords involving the treatment of non-chord tones.
Insufficient information to give it a definite name. We need more notes, or some context (a chord is often best described by what it DOES, not merely what it IS.)
You say 'the root is C'. All you really know is that the lowest note is C. Not at all the same thing.
It could be the bare bones of a Dm7. But we really don't know.
What does 'bound' mean? Tied up with ropes, a fence, a jump...? See what I mean? No context, no definite meaning.
I think what you call it should depend on how and where you use it.
There's Csus4 flavor in it, but my first idea when hearing it was F6omit3/C. Or Dm7(omit5)/C. Fm6omit3/C? Do you want to use it as a suspension? What other notes do you imagine that could be coming soon? If there's a melody that this chord is backing, what scale might the melody use? Where's the tonic? It could be anywhere.
If you think that this C+D+F chord is a sample that you trigger, it could fit a great variety of musical situations, and if you had to write a name for the harmony, the chord's name would depend on the context.