If a page is built with a <title> of, say, <title>'My site'</title> in the <head> and then altered to create another separate site, it is seemingly impossible to change the new site's <title> to, say, <title>My other site</title>.
Can you be more specific on what you mean by "altered to create another separate site"? There's not much you can "not" do with the Head areas, and you change those in the settings and that's very seldom not changeable.
Give some more information please on what you did to the page so we can better help you.
Thanks for the response but I found the solution just after you posted. It can be changed in the page's properties - Design > Pages > right click on a page > Properties.
Glad you worked it out, and yes that's where you change all page specific headings. You can also add global headings by going in the project's settings and setting it there. Then all pages will have that. Comes in handy for adding things like Google's codes for SEO etc.