Should NATO be reinvented as a more international organization?

At this point, it is becoming illogical to keep it as the North Atlantic Treaty Organization. We have allies in the southern part of the world, such as Australia and New Zealand, and that's kind of excluding them.

So why not reinvent it as something like PETO (Planet Earth Treaty Organization... lame name, I know.), getting all current NATO members and adding new ones such as Australia, Japan, and possibly Russia, along with future members of NATO (which I believe include Israel and Ukraine)