Can I change the domain name of an existing SquareSpace web site?

Site URL: http://naturetable.org.uk

Hello,

I have a SquareSpace web site (call it MySquareSpaceName.com ) and also an external domain name (MyPreferredName.org.uk) that is registered with Namecheap.  The domain name MyPreferredName.org.uk redirects to MySquareSpaceName.com. 

Suppose a user types in MyPreferredName.org.uk and is redirected to the web site on MySquareSpaceName.com .  After that, while the user browses the web site, the URL MySquareSpaceName.com appears in the user's address bar at the top of the browser.  I don't like this, but I don't know how to fix it.

Can I transfer the domain name MyPreferredName.org.uk to SquareSpace. and then attach that domain name to my web site? How?

Thanks

Bob

A further note: On the SquareSpace settings for my web site, it says I can "Use a Third-Party Domain". If I enter my preferred domain name, it says I can't transfer the name, because "org.uk domains are not currently supported".  However, it gives me the option to "Connect the domain to your Squarespace web site".  I don't understand what this does.  If I connect the domain, will it solve my problem of the old domain name being displayed?

I have transfer old domain my domain https://dokter-tht-spesialis.com to squarespace but it pending. I also have paid for 20USD. How can I activate ?