To add here, there's no "generic" solution for dealing with errors during installation. Depending on what caused the issue, there are some troubleshooting steps to follow. Thus, we would need to know the error code (if present), and more specifics regarding the environment where you are trying to install Bitdefender. Installations may fail for various reasons, OS requirements not met, other security solutions or firewalls installed, network issues, incompatibility in Windows S mode, administrative rights, and the list goes on. But the error code can give you a hint where to look.
As for Bitdefender not recognizing your license after install, the software may not be linked properly with your Central account where the license/subscription is running (assuming that it was successfully activated). Switching the account and re-entering your credentials in the Bitdefender app may help sync the product with your account. If this doesn't help, then something else is happening there.