I cringe whenever one of the higher-ups says "Jehovah", when anyone else, outside of the organisation, says "God". The name change could be possible. They probably couldn't have "church" in their title. Something like "Worldwide Congregations of the God of the Bible" might be enough to look more mainstream while maintaining some distinctiveness. Of course they might need to change the whole "New World Translation of the Holy Scriptures" title to something with "Bible" in it to facilitate a change of that sort.
There are plenty of naming possibilities. "New Life", "New Hope", and so on.
But a name change won't necessarily stick. Prince tried to be clever and ended up being "the singer formerly known as Prince". X is still called Twitter by most people. Be prepared for "the organisation formerly known as The Jehovah's Witnesses "