Do you email aliases? There are many ways to do this. Almost every email provider offers this service. Some domain registrar offer it for free as well, like porkbun.

I guess it depends on the domain registrar and the hosting which option is easiest. Also important; do you want to automate it or just do it manually?

I don't know of any out-of-the-box solutions, so I recommend starting out manually and then automating if there's enough demand to warrant the investment.

If you hook up your domain to something like Mailgun it's relatively straightforward to set up aliases.

As for payment and collecting customer information, it depends on whether you want to charge a one-time or recurring fee. In case of a one-time fee I'd look into setting up a Typeform with Stripe payment. For recurring payments, I'd look into Memberful. I don't know if they allow you to collect additional information (such as the alias the user wants), but you can always send them an email or Typeform link.

I'd start off doing this manually. If there's enough demand, look into automating it with Zapier or coding it up yourself.