No, that's not how it works. If you have registered the 2LD you have exclusive control of it, and only you can delegate a subdomain under it. However, a great number of common first and last names are reserved as 2LDs by the registry and cannot be registered by anyone; instead, third-level registrations under those 2LDs are available. Also, if someone does register a 3LD under a previously non-reserved 2LD, the 2LD will be reserved reactively so that no one can register it.