I think we have an explanation (at least according to Dole Soft Serve - and who doesn't trust everything they read on the internet?). The problem isn't using the name "Dole Whip" - the problem is when other sellers try to make the connection to the most famous purveyor of Dole Whips (Disney). From Dole Soft Serve's blog website
https://blog.dolesoftserve.com/2016/03/31/dole-whip-vs-dole-soft-serve/
"One of our strongest emotional connections with consumers is the iconic DOLE Whip treat, sold at Disney® parks, commonly in the form of a delicious float. Anyone who’s enjoyed DOLE Whip will instantly recognize the delicious taste and tropical flavors of DOLE Soft Serve – because they are, in fact, the same product! We just call them by different names, and here’s why.
Originally, the Dole Food Company made the DOLE Whip soft serve mix themselves. As demand grew, DOLE strategically licensed the brand to Kent Precision Foods Group, the leader in dry mix foods, who now exclusively produces the magical mix that makes DOLE Whip.
Outside of Disney Parks, the mix is sold and marketed as DOLE Soft Serve. Around the country, independent frozen yogurt shops (like Menchie’s) and tourist attractions (like Dodgers Stadium) serve DOLE Soft Serve. And since the name “DOLE Whip” is so familiar among consumers, we encourage the use of this alternate name on store signage, on menus or even for advertising.
However, “Disney” is a trademarked brand, and all its properties are protected by copyright. So when using the DOLE Whip or DOLE Soft Serve name, operators must avoid referring to or implying a connection to Disney to avoid pesky trademark infringement.
To sum up, the names “DOLE Soft Serve” and “DOLE Whip” can be used interchangeably."