When you create a document based on a template, the umbilical cord between
template and document is cut immediately as far as styles are concerned (the
document retains a connection to the template for access to toolbars,
shortcut keys, macros, etc.). You can update the template styles from the
document (by modifying the styles and checking the "Add to template" box),
but changing the styles in the template will not affect the document unless
you reattach the template (Tools | Templates and Add-ins) with
"Automatically update document styles" checked.

But even this would have no effect if you renamed the styles: Word would not
update styles in the document because they would all have different names
from the ones in the template. I'm afraid if you want to rename the styles
in the documents, you'll have to do it manually (although you might get some
help with a macro if you post in one of the Word VBA NGs).

--
Suzanne S. Barnhill
Microsoft MVP (Word)