The vinegar is altered by the lye. Sodium Acetate is created, which hardens the soap. In my experience, with my highly sensitive nose, I do not smell vinegar in my finished soap. I use white distilled vinegar, however, not ACV.
How to label the soap is based on your requirements in your geographical location. In the US, it may be 'what goes into the pot', in which case it would be 'vinegar', or 'what comes out of the pot', which would be water (because vinegar contains water) and sodium acetate. I cannot speak for other areas around the globe.