Remove existing Facebook account from OS X
My suggestion would be to log out of the current Facebook account. Then go into your user's Library folder (holding down the alt / opt key while in the "Go" menu in Finder and you will see a new entry "Library"). In your Library folder enter the subfolder "Preferences" and delete these two files:

com.apple.accountsd.plist &amp; com.apple.internetaccounts.plist (or just shove them over to the Desktop for testing)

Log out and back into the correct account and see if there are any notifications in Notification Center still listed. If yes, then download Onyx from http://www.titanium.free.fr/downloadonyx.php and let it do an automation where it clears all caches. When Onyx is done it will ask you to restart.

From here you should be good and there should be no trace of the original/old Facebook account. If however you notice anything still being left over, comment back with more information.