Sunomono means things (mono) of (no) vinegar (su), or vinegared dishes.
Sanbaizu gets its name from an old way of measuring. Ippai, nihai, sanbai means one bowl, two bowls, three bowls – hai (or pai/bai) is the specific Japanese counter suffix for bowls. When measuring out liquid ingredients for sumono, people would traditionally use very small sake cups, so sanbaizu was originally a vinegar sauce made up of one small sake bowl of each of the typical sumono ingredients: vinegar, mirin and soy sauce. Over time the recipe ingredients and ratio changed a little, but the name stayed the same. There is also a traditional nihaizu consisting of equal parts of vinegar and soy sauce.
If it’s hard to get your hands on some high quality mirin, or you don’t want to use it for any other reason, you can substitute it with 1/3 the amount of sugar.