Chord naming gets complicated smile I agree with Matt, you'd need to know the context, but even then it can still be open to interpretation, is this a solo guitarist or full band, it all makes a difference and at the end of the day it's more about giving the other musicians an idea of how the chords should be moving harmonically. When you name a chord anything other than what it actually is, then there's really no way of knowing the chord's intention unless it is explicitly written. Play something in the wrong inversion and it can sound completely wrong. This is the problem with chord books as opposed to actual notation.

A few points here about this chord - first off, the C major triad is already well established, it's not easy to "un-hear". Those four notes alone can really only be two things, C/F or Cadd11. If F is in the bass I'd call it C/F, anything else I'd call it Cadd11. If this was a six note chord then I might think differently, but if we aren't told what the other two notes are then we can only work with what we have.

Sus chords have a suspended third and nothing else, although modern interpretations will use the term for the replacement of other scale degrees (sus7 for example) - technically it's not correct but I guess things evolve wrong or right. The whole point of a Sus4 chord was to add suspension intended to be resolved to the major 3rd. In modern music Sus4 chords do not always resolve so it has become a chord in its own right - this brings another problem.. Sus2 chords?

Again, (technically) they don't exist because they are just inversions of Sus4 chords, eg. Fsus2 is just a Csus4 inverted. This is where context comes in. If we have a chord progression that goes C, F, G but the C is played with a D instead of E then it probably makes more sense to call it a Sus 2 because we'll just think of it as a modified C because the overall sound is still a I-IV-V ... but again, technically, and pedantically, it's still kind of a Sus4 simply because there's not much suspension in a whole tone as there is in a semitone. A better name for sus2 is probably "add9, no 3rd" but who'd want to call it that.

Fmaj7sus2? If you were ever going to name it that, then there cannot be an A in the chord - if there is then it isn't suspended. If it also included the 3rd then it's an Fmaj9. If it doesn't then it becomes difficult to NOT hear the fact it's dominated by a C major triad. This, in my opinion, makes it a chord name that just sounds wrong. So in short, in isolation played on a single instrument, I think it would be difficult to name it anything other than C/F or Cadd11. In a full band context I would expect somebody else is probably playing the M3rd - in which case it's an Fmaj9 - but if they weren't then I'd expect the maj3rd to sound OK if it were added - if it didn't, then it's probably not meant to be any form of F major.

This is why it all gets so complicated - all of the above is open to opinion and interpretation. Bottom line - a chord cannot be anything other than the notes it contains - if it is intended to have a different function then this can never be done with just a basic chord name, it's either notated properly or it's left to the musician to make their own mind up - and this will always lead to differences of opinion.

All my opinion of course smile