LLMs disambiguate "your brand" from "every other brand called that" by cross-referencing the Organization / Person / Product entities you declare across your pages. If your homepage says "Acme Corp" and your blog says "Acme" and your About page says "Acme Corporation LLC," the entity graph splits three ways and the LLM grounds on whichever surfaced most often in training.
The checker fetches your sitemap, samples up to 20 URLs, and extracts entity signals from each. Matching NAP / sameAs / author-name signals are cross-compared for drift.