Tummy tuck that creates very small waist, is there a name for that?

Unfortunately, you
have not provided any photographs but often the limiting factor in making a very
small waist is intra-abdominal fat. 
Attempts to tighten external abdominal wall will compress the internal
fat, raising the diaphragm, which interferes with breathing.  However, if that is not your situation, the
technique I recommend is abdominoplasty with mesh reinforcement combined with
liposuction.  The key feature of an
abdominoplasty is not tightening the muscles but tightening the lining of the
muscles, which is called the fascia. 
After the fascia is tightened I will reinforce this with mesh to create
a more hourglass figure.  Liposuction of
the flanks and sides also helps decrease the circumference.  Best Wishes,Gary Horndeski, M.D.

Yes, a good one!  Seriously though, a tummy tuck should be able to remove excess skin, fat, tighten muscles and restore your underlying waist line.

Of course there is a limit to your waist size that is determined genetically and you must be at ideal body weight. The surgeon helps by doing liposuction in the muffin top areas to give you more of an hourglass figure. The tummy tuck removes skin, fat, and provides muscle tightening that also helps cinch the waistline. I am not aware of a name for a specific procedure that reduces waist size but any such procedure will make use of liposuction and a tummy tuck. It is important for the surgeon not to be too aggressive with the liposuction because this can leave contour deformities that are difficult to correct. I have attached a link to my website in case you wish to look at some examples.