One way to solve this is to host on a Windows server instead of Unix based. Windows is inherently case-insensitive, Unix the opposite. One work-around might be to set up PHP redirects. To do that you'd have to set up directories for each variation you wanted to catch. E.g.
example.com/ClientName/
example.com/clientname/
Then in the "dummy" director(ies) put an index.php something like:
<?php
header( 'Location: http://www.example.com/ClientName/index.html' ) ;
exit;
?>
<!DOCTYPE HTML>
<html>
<head>
<meta charset="UTF-8">
<title>URL Error</title>
</head>
<body>
<h1>URL Error</h1>
The site address has been entered incorrectly. If your browser does not automatically redirect you, please click <a href="../ClientName/index.html">here</a> to continue...
</body>
</html>
Note: You must NOT precede this with ANY code, not even a blank line.
P.S. There are a number of other ways to redirect users, but I use PHP because:
a) It is handled by your server, so is not dependent on the user's browser.
b) It does not require changes to the server's htaccess file.
c) Using the HTML <meta> redirect is frowned upon.
See http://www.wikihow.com/Redirect-a-URL for details of other ways...