Sorry, I don't understand this rule, would someone kindly explain?

I own lastname.name and use it for email only like this: [email protected]

I always thought as owner of lastname.name, I'm the only one able to add subdomain.lastname.name. Is this wrong??

1) Can anyone "buy" scam.lastname.name without my authorization on .name??

2) Can anyone owning not.lastname.name then steal my emails going to: firstname@*.lastname.name or even [email protected]??

BUT: If someone ONLY bought not.lastname.name and doesn't own lastname.name, they'll get terminated. Would that be 'good' as it would stop 1) and 2) ??

I'm really concerned. My family is using [email protected] as the personal email, I'm hosting and paying for since many years.