I'm not sure what you mean when you say "...that's what I want peopleto see when they get to the site". Are you talking about the browser tab? Or the address bar? Or the web page itself?
The answer depends on what you are looking for.
The page title will appear in the browser tab.
The web page will show whatever you put into your design.
The address bar will not show the page name - when someone opens your website, the server looks in your website root directory (public_html) for the home page which must have a file name of index.html or default.html. That's just the way host servers work.
(technically, you can use .php or .asp extensions for you home page file name as well - if they are dynamic pages.)
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