It used to require moving the domain first
Connecting a domain you already had registered elsewhere used to mean extra steps before you could actually use it with your site.
Now you add it yourself, from your panel
In your site settings, under "Change domain", type in the domain you already own - no http:// or www - and Speaksite connects it. The security certificate (SSL) is generated automatically, and you can see it marked as active on the same screen.
There's no need to transfer the domain itself or do anything beyond pointing its DNS where the screen tells you to.