If its an Onion (Tor) hostname, you absolutely do own it. Sure, its not memorable being a 128 bit hash. And nobody else can impersonate nor take.

And for lower bandwidth tasks, Tor Onions can't be beat. Just make sure to use 2fa on services you offer to keep the trash out. Things like fail2ban don't work the way you intend.

Let me just require a phone number for my totally anonymous drug-market service