There is no way to definitively tell who owns a relay. They don't even have an associated npub; they're just websocket addresses, to the users.

The ones with whitelists and AUTH (community and/or paid) are self-explanatory.

The "public" ones also have restrictions, but they tend to obfuscate them. And they are prone to rate-limiting and throttling of particular npubs, rather than allowing/disallowing them outright.