Why ChatGPT names some brands and not others
The model is not searching your site. It is drawing on what it learned during training plus, in browsing mode, whatever it can retrieve live. Both routes reward the same thing: being described the same way in enough places that the association becomes reliable.
If your brand is described three different ways across your site, your LinkedIn, your press coverage and your directory listings, none of those descriptions is strong enough to stick.
The three things that actually move it
First, entity consistency. One brand name, one category phrase, one location, repeated identically across your site, your schema, your socials and every listing. Organisation schema with sameAs links pointing at your real profiles does the connecting work.
Second, third-party coverage. Models weight sources they consider reliable. Getting written about on established publications, industry sites and well-maintained directories puts your name in the training and retrieval pool. This is why online PR and AI visibility are the same job now.
Third, extractable answers. Pages that state a fact in one clean sentence get quoted. Pages that bury the answer in three paragraphs of preamble do not.
How long it takes
Browsing and retrieval-based mentions can appear within weeks of publishing and getting cited. Mentions that come from the model itself, without browsing, lag by however long it takes for a new training cut to include your coverage. Plan on months rather than days, and measure both separately.