One problem that guitarists (and it seems to be unique to guitarists) face is that they tend to want to name every shape they play without considering the actual musical theory surrounding the full score or arrangement.

First, a suspension is often NOT a chord, it is a harmonic event over time. In contrapuntal music, a suspension imeans creating a tension between two harmonic structures by holding over one note while the underlying harmony shifts. The suspended note then resolves downward into the new harmonic structure.

If that is not happening in the composition, then you aren't playing a suspension in this somewhat normative sense. The shape you are playing is not a chord in and of itself.

More modern music borrowed the term "suspension' (though oddly, not retardation for some reason) to mean chords where the 3rd is omitted but there is no resolution downward to the following harmonic structure. But even in these cases, the third is often implied by other instruments or vocals, in which case it is still not a suspended chord even in the modern sense as the harmonic structure always includes the full score and not merely on one instrument.

So, n many situations where a guitarist is playing the 1, 2 and 5 tones of the underlying scale, the base, piano, horns or even the vocalist is hitting the 3. The harmonic structure contains the 1, 2, 3 and 5.

If the 2 is in the same octave as the tonic, this is an add2 chord for the harmony. If the 2 is in a different octave (usually the octave above the tonic, though not in some inverted chord forms) it is referred to as an add9.