Big Bang makes it sound like you have a large object and then it exploded with a bang. But there was no explosion since explosions can't occur faster than the speed of light, and there was no bang since there is no sound in space, and no magical large object that exploded.
What happened was that the universe was more condensed than what it is now. It was so condense that matter did not exist as we know it, there was just too much energy per space. Then all this energy cause space to expand rapidly, when the space expanded rapidly it cools since there is less energy per unit of space, this cooling allowed the gluons to form, then atoms, then gas, then gravity pull the gas together to make stars, and gas giants. Then some of the stars went supernova and produce heavier elements and some collapsed into black holes. A very oversimplified explanation, but it helps prove my argument that it should be called the Great Spatial Expansion.
It sounds way cooler, not only does it sound cooler it really helps to understand what this event is, Great Spatial Expansion pretty much hits the head on the nail, space expands. And one day it will collapse concidering the theory be true. At that point, it can be called The Great Spacial Collapse
I've known alot of christian science deniers who think the big bang is an explosion when a 2 second google search would say it's the expansion of space itself that's happening to this very moment. The Great Spacial expansion is a much better word and would help some people become more knowledgable on the subject.
An overly technical definition would turn all but the most hardened geeks away. Another thing would be that, in celestial terms, this happened very quickly. Calling it "The Great Spatial Expansion" makes it sound like something out of a cheesy sci-fi flick that we'd see on Friday night. So while it would more accurately define it, simply appending the definition after it in a dictionary would suffice.