You can create a Facebook page for any topic of interest that you may have. When you create a page, you choose a name for that page. However, names aren't exclusive to one group, allowing for the creation of more than one group with the same name. If you delete your Facebook page, you can re-create it and reuse the name from your previous group without any trouble.
Delete Facebook Page
Log in to your Facebook account.
Click the “More” link next to “Pages” in the left menu. You will see a list of your Facebook pages.
Click the name of the Facebook page from the list to navigate to the page.
Click the “Edit Page” button and navigate to “Management Permissions.”
Click the “Permanently Delete” link at the bottom of the page.
Click the “Delete” button on the pop-up window to confirm. You will return to your list of Facebook pages.
Create New Facebook Page
Click the “Create a Page” button.
Select the category for your page, then type in the name of the page in the text box. You can reuse the name from your old page.
Place a check in the box next to “I agree to Facebook Pages Terms,” and click the “Get Started” button. You've re-created your Facebook page using the same page name that you had before.