It is not clear which thread you are talking about and your platform.
gRPC core does set thread names if applicable. For example the sync server will set its threads with name "grpcpp_sync_server" in thread_manager.cc. For linux, the name is set to the pthread if GPR_LINUX_PTHREAD_NAME macro is set.
If you use the gpr_log functions the current thread id will be logged, which is a way for you to tell which thread the log is generated from.
If you really want to set some thread name of your own, I guess you can (for linux) maybe use pthread_setname_np in your method handler? You can use gRPC's thd_posix.cc as an example.