I created a different theme of twentyten (fork) and not really a child of twentyten?
Yes. It is important to differentiate between the two types of theme customisation - especially when posting here as, otherwise, people will start making incorrect assumptions.
I can continue to keep this theme and rename the directory to something else that does not reflect "child" of twentyten.
Yes but you will not benefit from any future updates to Twenty Ten if you take the "fork" route.
how do I adjust?
If you want to change it on the main posts page, you'll need to edit index.php. In single posts, it's single.php. Theme Development has a simple overview of what template is applied when that you might find helpful.
Additionally, you need to edit the
twentyten_posted_on() function in functions.php as this is what generates the post date.