You can change the name of your Facebook page but in order to do so, you need to be an admin for that page. If you originally created the Page, you automatically become the Page’s admin. If you’re not sure if you are the admin, you can check by clicking “Settings” at the top of your page followed by “Page Roles” in the left. Once you confirm, then you just click “About” on the left side of your Page, click “Edit” next to your Page’s name, enter a new Page name and click “Continue”, then click “Request Change”.
It’s worth noting that if you don’t see the option to edit your page's name, it may be because this option isn’t available yet in your location, there may be limits on your Page, or you are trying to change the name of a Regional Page that falls under a Global Page.