(as I understand it)
The GDPR rights to be forgotten are not transitive. Requesting one company to forget about you does not require them to take action to have your information removed at other companies, even those they have shared your information with. In fact for them to be able to have your information removed from another company would be contrary to some principles of the GDPR about accurate processing of information in the interests of the person whose information it is.
I also think most companies are unlikely to do this if the information was shared for some business trading relationship (eg frequent flyer alliance, marketing details passed to other companies, etc). They probably will remove it if it was shared as part of a service provider agreement (example: the company uses a customer-relations-as-a-service provider and will cause your information to be removed from customer-relations service).