Does anyone know how to get this look with buttercream?  I'm interested in replicating the vertical lines on the cake side.  I tried an impression mat, but lots of mess and not very deep lines.  Do you think it is piped??  Should I use crusting buttercream? Or does this look like fondant (which my client does NOT want!)  Thanks in advance. :)

It is fondant judging by the texture and the evenly cut lines at the top. I'm not sure how you would replicate this is butter cream, maybe a round tip 3 or 4 depending on the thickness of the lines you want, but if you don't have a steady hand, straight lines are hard, especially vertically. There are some things that just can't be done in butter cream, unfortunately. 

I agree that this would look better in fondant than buttercream.  Maybe you could try a frozen butter cream transfer method though.  Maybe meaure out a sheet of wax paper as tall as the cake and as long as the circumference.  Mark it up with vertical stripes, flip it over and pipe on buttercream using those lines as a guide.  Put it in the freezer to harden up.  Wrap the wax paper around the cake, adhering the buttercream stripes to the cake? Maybe?

Unfortunately customers cannot always have things the way they want them.  This look requires fondant...and it's not easy to get perfect...but buttercream would be a nightmare.  I try to encourage bakers never to attempt something they're uncomfortable doing just to make a sale.  Simply explain this option requires fondant...either accept this or choose a different design.  If not, you might need to decline the order.

this is what i would try first -- i would use two dowel the same size as the stripe I wanted -- roll roll roll roll 20,000 fondant sausages inside the two dowel so they all come out exactly the same -- line them up on something that was inflexible -- straightening each one with a ruler so it's laying perfectly straight -- I would cut the bottom ends so they were more even -- chill them in the fridge for a bit -- apply each one to the cake lining up the cut ends on the bottom edge of the cake -- but they would be raggedy around the top -- then take a sharp little knife and cut them all across the top holding my breath --

but I would also test to see if I needed them chilled for sure -- might not need them chilled -- and I would test cutting the top edge straight before I applied them all --

but yes you need to practice this before you take an order for it

What is the name of this design . And does anyone have a tutorial on how to do it ?

i don't know of a specific name for it --