I’m very rigorous about including the full domain name in my email address (consistency helps me remember what I used. I made the mistake early on of using myname-paypal@mydomain.com instead of myname-paypal.com@… and it drove me insane until I changed it), but every once in a while there’s a site (or occasionally a customer service rep) that refuses to accept that, in which case I just make up some unique three letter suffix to use instead and make a note of it in my password manager. My email for my kids’ school whose name starts with a W, for example, just ended up being mynane-w@mydomain.com. Luckily these exceptions are rarely necessary and I’ve only had to do half a dozen of them in about 17 years of doing this.
And I had no way to apply for the government licence thing I needed, and the people on the phone suggested I use the website.