Follow these steps to change your site name:
1. Go to My Site(s) → Settings or just click here: https://wordpress.com/settings/general/
2. Under the General tab, change the value of the Site Title field and click SAVE SETTINGS
re: Deleting Site
It is not a good option because, if you delete your site the address(URL) associated with the site will be reserved due to which no one will be able to use that address again(not even you).
If you want to delete every content of the site by keeping you current blog address and start over, emptying the site would be a good option instead of deleting it.
Hope this helps! 🙂