How to point the third-party domain to own subdomains and build the great infrastructure for that?

Intro:

Right now I am working on the web-builder site that allows generating the own websites.

The websites that will be generated will have the own subdomains.

Example:

1. https://webbuildercompany.com - the core website;
2. https://businessname1.webbuildercompany.com - the business site that will be generated by some "business company 1".
3. https://businessname2.webbuildercompany.com - the business site that will be generated by some "business company 2".

Questions:

How to allow the customer to buy own subdomains like https://businessname1.com and point it to https://businessname1.webbuildercompany.com?

What should be done in order to set up that?

What is the best practice to do the infrastructure for that?

How are the worldwide companies (like WIX) doing the same?