Usually one company will own the trademarks and license them to the other, so only one of the companies is responsible for managing the IP. E.g. the Rolls-Royce

Usually one company will own the trademarks and license them to the other, so only one of the companies is responsible for managing the IP. E.g. the Rolls-Royce IP is owned by Rolls-Royce (the aerospace company) and licensed to the company that builds Rolls-Royce-branded cars (currently BMW). The contracts probably stipulate whether and how the spin-off has to handle a logo redesign or whatever else.