Change the name of the root name of an already built Wordpress theme

Question

If I have built a site using an existing theme (i.e. "Twenty-Ten"), but then modified it considerably and want to re-name it entirely, how would I go about doing this without breaking all the links? I know I can simply text-edit the style.css to change the name there, but I'm referring to the root all throughout the install:

<link rel='stylesheet' href='http://myWebsite.com/wp-content/themes/CURRENTTHEMENAME/styles/style.css" />

to ....

<link rel='stylesheet' href='http://myWebsite.com/wp-content/themes/NEWTHEMENAME/styles/style.css" />