Michelin also owns Uniroyal. Uniroyal and BF Goodrich merged long before Michelin bought them.
Also General is owned by Continental.
The big domestic tire makers used to be Firestone (now owned by Bridgestone), BF Goodrich (now owned by Michelin), Uniroyal (now owned by Michelin), General (now owned by Continental) and Goodyear.
I've lost track of some of the lesser know American brands but here are some of them: Armstrong (now owned by Pirelli), Kelley Springfield (always or for more years than I can remember, owned by Goodyear), Dayton (owned by Firestone), Cooper, and Fisk. At the moment I can't remember the name of the company that makes Futura (Pep Boys house brand).