Yes, if you pay for {lastname}.name, the full domain is yours, including whatever you want to do with subdomains. However, .name also allowed direct registration of third level domains ({firstname}.{lastname}.name). These were mutually exclusive by domain… so if somebody registers the 3rd level, nobody can directly buy the 2nd level, and vise versa. As far as I understand, it was first come first serve based on the 2nd level domain.
There were also some shenanigans around automatic email routing in that case.
There were also some shenanigans around automatic email routing in that case.