Whether an unlinked mention of your brand helps ranking is unconfirmed. Google does confirm that its site name system, which picks the name shown beside each result, uses "references to it that appear on the web". For news publishers, Top Stories now has a documented, user-driven lever: a searcher can pick preferred sources, whose content is then "more likely to appear in Top Stories" with a "preferred" badge, and is also badged in AI Mode and AI Overviews. Only domain and subdomain sites qualify, and you may invite readers with a deep link.
<a href="https://www.google.com/preferences/source?q=example.com">Add as preferred source</a>