It's easy to create and train a model to distinguish between brands and generic words by counting how many times a single word appears over app descriptions, for example - there are countless ways to do this. This, in turn, can neutralize the effect of naming your app after a generic word when it comes to search ranking.

This would be quite funny. I still see businesses called things like AAA automotive and similar which date back to optimising their telephone book listing order. Was this early SEO?

But if there's too much uncertainty then just don't do ads at all. The fallback shouldn't be ads for all search terms.

Your post seems like a rebuttal to the idea of "just show the app they wanted", but that wasn't the request. The request was just to leave the search alone.