I think that tells you something about the plausibility of this business model.
The Scoop Nazi
=d&r=
2 Cooks 1 Bowl
There’s a St. Louis strip mall restaurant that underwent a menu change without a name change. Their sign now reads Hot Pot (and in smaller type below) Smoothie Shop.
As for the OP, Soups & Cones seems like name people could say without trouble.
(Bolding mine)
No, really. There aren’t.
Pleasurable Cream
Whoa. Way too many porn images with this one. 
J.
Yep, it’s my choice as well although Czarcasm’s Scoop And Crackers is pretty cute too.
Soup or Sundae. (think football)
If the business is in New Jersey or you want to go with a NJ theme, you could call it “Yo, I got yer effin’ Ice Cream RIGHT HERE!” unless it’s winter. Then you could call it “Yo, I got yer effin’ soup RIGHT HERE!”
Scream.
Souper Dipper
Frost & Broth