The first thing we thought we could use it for was an gallery of React Native components. Or, you might say, an "expo" of "components" --> exponent.
We also liked the idea of a non linear increase in developer productivity and thought it sounded cool! It has the right level of nerdiness for a product that is mostly about software developers.
After that, we spent a couple of nights trying to think of a better name but we couldn't come up with anything better so now we're kind of stuck with it.