Own the domain put catch-all for that domain. No need to generate anything.

A few ways I've heard about - DuckDuckGo.com has a system that generates a random email address on their domain where you can request "a new email address" whenever you need one; you request a new alias and they create a permanent mapping to your real address from that new address. Then mail sent to say Foo-Bar-Hotdog@duck.com goes to you, duck remembers the mapping that this goes to your address. You can reply back and duck handles the anon mapping.

Or you can have a catchall email address on your own domain, where anything sent to any alias on your domain gets forwarded to your own address. Then hamburger@myDomain.com and mcdonalds@myDomain.com goes to your real private address. you don't have to set it up. Anytime you join a new service, say reddit, you tell them your address is "reddit@myDomain.com".

All of these have a level of pain associated with them. And they aren't that private. The government could no doubt get a court order to pierce the obscured email addresses.

There's proton email and many others. All of these are too painful for most people.

I have wondered if people who want to be really secret set up a chain of these anon mail forwarding systems.

Fastmail will let you create any number of "aliases" as they call them, with not too much friction.

Theoretically, the easiest way is to use a sub address (more commonly/colloquially known as email aliases or plus addresses, they're described in RFC 5233). You should be able to add a separator character (usually a plus, sometimes other characters instead/in addition) and arbitrary text to your email address, i.e. "myemail+somecompany@example.com" should route to "myemail@example.com"

In practice, this works about 95-99% of the time. Some websites will refuse the + as an invalid special character, and the worst of the worst will silently strip it before persisting it, and may or may not strip it when you input your email another time (such as when you're logging in or recovering your password).

I also suspect spammers strip out subaddresses frequently, very little of the spam I receive includes the subaddress.

So the only 100% reliable way is to use your own domain, but you don't need to run your own custom mail server

Proton let's me bring my own subdomain for those random emails and does a pretty good job of tracking which email is given to whom, and also supports hiding your email even if you want to initiate the email contact, not just reply (plus scheme in mail address doesn't allow this). Otherwise you can also use their domain too, to stay fully anonymous.

So far I've been happy. I hope I'll stay happy.

If you’re on Gmail, there’s “plus addressing” - this allows you to append any term after your email - and then sort accordingly.

So if your Gmail is foo.bar@gmail.com you can use foo.bar+servicename@gmail.com and the mail will still end up in your mailbox. Then you can create a rule that sorts incoming mails accordingly.

I use addy.io