Every so often I meet a person who works for a company or nonprofit that has an acronym for a name. Too often when I ask what the acronym stands for they answer, “It doesn’t mean anything.” They might add, “it used to, but we moved away from that.”

There’s a better answer and a better way to extend your brand when an inquiring mind wants to know.
First option is to answer like this:
“That acronym reflects our beginnings when (insert your acronym here) stood for our founders (or whatever it stood for). Since that time we have changed our focus a bit but the history of the organization lives on.”
The second option is to change the name.
Change it to something that means something now if you are trying to distance yourself from the old reputation or the old mission. Reinvent and rebrand the corporation confidently; without worry that people will be confused, or hate the new name. There is such a thing as a successful name change. You might remember when GTE became Verizon. You might not like the name, but it didn’t flop like Coca-Cola fooling around with a very successful recipe (still a mind-boggling move).
If you go with route one, then make sure people can learn about the history if they want. Add a section under your ABOUT US page on your website that explains your name and why it’s important. Educate your employees (in a fun way) so they learn the history and can speak about it intelligently.
Changing your name is a much larger undertaking and it really is a re-branding project. Allocate a decent amount of marketing funds for a comprehensive rollout of a new name. Use all your tools and outlets available to explain it as a name change, not a hostile take over. You need a full court press to ease the transition successfully and that will take some resources.

Whether your name is old or new, it means something and answering a question about that meaning is a perfect introduction to talk about what your organization does. Take advantage of this great opportunity.