I need to "close" my old squarespace site and open a new one.

Site URL: https://www.sarahincheyphotography.com/

I used SquareSpace to create  a website called SaraHincheyPhotography (that's my name).  I didn't realize there was another Sarah Hinchey in Massachusetts who is also a photographer, using the website SarahHincheyPhotography.com (not on squarespace).  I am willing to change my business name. and have come up with a new name, but her lawyer has sent a cease and desist letter demanding that I completely remove all the content from my website from public access.  I am willing to do this, but don't know how.  I'd rather not create a new website from scratch if at all possible.  Any guidance is appreciated.  Thank you!

If you are rebranding your site, you'll usually change the site title and the domain name first.

Once you've purchased the domain name, you can connect this to the site and remove the old one. To remove your domain you must first add the new one, or set the primary domain to be the built-in Squarespace one. This support article may help: Setting a primary domain.

If your site has been added to search engine results, you may also need to remove your old site name from these. For help with this see Verifying your site with Google Search Console and Verifying your site with Bing Webmaster Tools.