I'm sure Google uses their knowledge graph to determine brands. In other words, you can't brand to Google, your searchers must ask for your brand via Google. That would be a strong signal to Google that you should rank even higher, because searchers resorting to adding the brand to a query feel like Google won't give them the results unless they goose the search.
Pretend you're Google. People start searching for Widget1 Quicklime, Widget2 Quicklime, etc. and you see that. Isn't that a good signal that people like something called "Quicklime" and Google isn't giving searchers what they want? As soon as Google figures out that Quicklime (I made that up, BTW) maps to Quicklime.com, the brand is established.