The correlation is real
Compare two sites with similar link profiles and one with far higher branded search volume. The branded one almost always ranks better on generic terms. It is one of the most reliable patterns in competitive analysis.
Whether that is causal or a proxy for everything else a strong brand has, the practical advice is the same: build the brand.
What it does to click behaviour
When your name appears in a results page full of unknowns, people click it. That behaviour, aggregated, is exactly what a search engine is trying to learn from.
It also protects you from AI Overviews, because people searching your brand name are not looking for a summary of a topic.
How to grow it
PR, creators, paid social and anything that puts your name in front of people who are not searching yet. Brand search is the lagging indicator of demand generation, so treat it as your scoreboard rather than your lever.