Yes, there is a name for it, but maybe your overlooking it, because it's so obvious.
It would be much clear put into a basic context, like this for example...
When the tones
F are chord tones in the chord before, like a
G7, then the thing that is happening is called a suspension. That's the source of the
sus label, it's an abbreviation of the word suspension.
To have a proper suspension you precede the occurrences of dissonant tones like
F over a
C bass with those tone as chord tones like
F in a
G7 chord in what would be called a "preparation". The formal model is preparation, suspension, and resolution. Your example only gives the suspension and resolution parts of the formal model, but a suspension is so very, very familiar that you can hear a suspension without the formality of preparation.
Depending on what exactly happens before the
Csus you might have something other than a suspension, but that will only be a difference in classifying it more specifically. Without that preceding stuff, generically you would just call the
Csus "non-chord tones" that "resolve" to the plain triad
But it's also incredibly familiar. Is there a name for this? Or some song which might have stuck it in my consciousness?
This kind of musical "device" it too broadly used to name any specific song. It's broad to level of terms like "cadence" or "chord progression" except that this device is particular to melody. Terminology about melody seems less familiar to the average person who isn't a music theory nerd compared with many familiar terms related to harmony (chords.)
FWIW, you might be thinking the matter is about chords, because you're using a chord symbol -
Csus - and indeed you might play this in accompaniment not the song's melody. But, keep in mind I'm just explaining terminology, the label you can use for it, and historically the origin of the terminology comes from its use in melody and counterpoint, back in the Renaissance and Baroque eras.