Comment by flaminHotSpeedo

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