Your home page must be index dot something but it does not have to be index dot html. You have a few different options for your home page file name, which are as follows:
Any of the above file names will work. However you should note that they are all lower case. Index will not work because the "I" is upper case. It must be index all lower case.
What if I put all of the above file names into my directory, which one will show up?
The server will look for an index page in the same order as they are listed above, first checking for index.shtml and if it's not found it will proceed to look for index.shtm so on and so forth until it finds one. The first index page it finds is the one it will use.
Does this mean I should name my home page index.shtml since the server will look for that first?
No. ONLY use the .shtml extension if you are using Server Side Includes (SSI). Otherwise it is recommended that you use the .html or .htm extensions. Using extensions other than .htm or .html when there is no need to will actually slow your site down and not speed it up. The other extensions are telling the server it will need to do other work to the page before it can show it to your visitors, if there is no other work to be done then there is no reason to wait for the server to look for those types of commands.