Thanks for the reply. The site isn't live but on almost all Squarespace templates I can see the site name is in the top left corner of the header (or centre page top) and then appears on all subsequent site pages that are created. There appears to be no option when editing the header to remove the site title - leaving it blank is not possible, though I can see I can add a logo (don't have one to add).
Not sure why it's not obvious to edit individual pages to remove the site name from the header.