It's not possible to set up a custom booking URL to match your domain name, all booking page URLs will end in .youcanbook.me
To have a custom URL, embed your booking page into your own website using Embed Script. You can create whatever domain/page you want, and embed a full page with code for your YouCanBook.me booking page. Users won't see any difference, and you have full control over the page itself.
To get the embed code, go to your Dashboard, then click on Edit Settings Share & Embed, then click Embed on the modal, and Copy Embed code.