Give Google an entity to recognise
Organisation schema on your homepage with name, url, logo, description, address and sameAs links to your social profiles is the foundation. The sameAs array is the part most sites omit and it is the part that does the connecting.
Add founder, foundingDate and areaServed if they apply. More verifiable structured facts means more confidence.
Corroborate it off-site
Wikipedia and Wikidata carry weight but are not required and should never be gamed. Crunchbase, Companies House, LinkedIn, trade directories and consistent press mentions all contribute.
The requirement is agreement. Google needs several independent sources saying the same things about you.
Then claim it
Once a panel appears, use Google’s own verification flow to claim it. That gives you the ability to suggest edits, which is the only direct control you get.