For all the 100+ years of branding / preaching:
Most people think they are called "Jehovah Witnesses", not "Jehovah's Witnesses"
Most people only know "no blood" and "give out watchtowers". That's it.
Some know about shunning and child abuse scandals
Do they need to change their name? They would throw away everything that they have achieved in the last 100+ years which is ... well, what exactly? Nothing!
They could call themselves the Church of the Lard-Ass Gay Saints and no one would pay them any attention.
Personally, and completely selfishly as someone with the jehovahs-witness.com domain name, I think they should always call themselves Jehovahs Witnesses but it's interesting that they are known more and more as "the org" or JW.Org - Jehovah, the name they are meant to proclaim, now only gets an initial while the "org" part gets more focus.