Earlier quoted context omitted.
To do something similar as an individual, I highly recommend 33mail.com [1], which provides a generous free tier, and lets you supply arbitrary . As well as knowing where a leak originated, you can easily block any inbound email address if it is being abused. Not affiliated, just a happy long-time paying customer. [1] http://33mail.com/rj37w3
I do the same without using 33mail. I have my mail hosted on zoho mail which gives me infinite aliases that get redirected to my main address and in case I ever need to forward a mail from an alias I can create a new address with that alias, use it and then delete it. So when I register to a new site I usually input @mydomain.com and then if I want I can create a filter to sort them automatically
businessname@mydomain.io
Already caught a few selling my info