It's often called plus addressing. Quite a common feature in mail servers and mail services. MyName+<any-random-text> at gmail.com ends up in MyName's mailbox.
Doesn't that defeat the purpose? Surely anyone savvy enough to be dealing in black-market e-mail address lists is savvy enough to just remove everything after the + sign?
Probably yes. The software I'm using supports configuring the character per domain, so I can use say . instead of +, so I could use myname.service@example.com which I assume would solve that.