What name does the Homepage of the domain with Linux Hosting need to have?

Once you have created the website locally you need to check if there is a default document.
A default document is the first page of the website, in other words the HomePage, which has one of these names

index.html
index.htm
index.php
index.shtml

The order in which they are listed is the priority order in the visualization: if there is an index.html the following name will not be automatically visible.
Therefore by clicking
http://www.yourdomain.com
the page http://www.yourdomain.com/index.html will open automatically

In absence of the index the website will not be viewed.
You need to pay attention to the files names, how they are named in the page codes, because on Linux we are on a sensitive case environment or rather Capital letters are different to small letters, as Index.html is different to index.html.