You can follow these quick steps to change website name on Squarespace.
#1. First, access your edit mode
Suppose your site is: elf.squarespace.com
You can add /config after to access edit mode, so the url will be:
elf.squarespace.com/config
#2. Next, click Edit on the top left of the site.
#3. Click Edit Site Header
#4. Next, you choose SITE TITLE & LOGO then click on the Edit icon
#5. A box will appear, on SITE TITLE you can change your new website name
#6. Then, you click SAVE on the top left of the screen.