Git with Drupal 7 multi-site, naming directories
You don't need to consider a whacky git-based solution to this, Drupal has you covered.

Just uses aliases in sites.php, and use whatever method you like (assume-unchanged in the index, .gitignore, whatever) to keep sites.php out of the repo.

So on your local machine your sites.php might contain

$sites['website-one.dev'] = 'website-one';
$sites['website-two.dev'] = 'website-two';


And on a remote server:

$sites['website-one.staging'] = 'website-one';
$sites['website-two.staging'] = 'website-two';


And prod:

$sites['website-one.com'] = 'website-one';
$sites['website-two.com'] = 'website-two';


All the while, your sites live in 'website-one' and 'website-two' respectively; no need for tricks.

If you don't want to consider a Drupal-based solution, and still want to use git, I'd advise taking this over to Stack Overflow where such a question would be on-topic.