Changing Icloud user name
The issue is with the Apple ID used to activate the iCloud Service. An Apple ID is simply an email address that you sign into Apple with and, by extension, use set up Apple’s auxilary services (iCloud, iTunes Store Purchases, etc). 


  Is there a way to delete that old account?


Apple usually won’t let you delete an old Apple ID. You need to contact Apple ID Support to inquire. If you wish to purge Apple’s servers of all the information associated with that Apple ID, you can.


  Is there a way to…recreate a new account with my new email address?


Yes. 

Option One:

Create a new Apple ID using your new email address. This is the easiest solution.

Option Two:

Change the primary email address associated with your Apple ID account. You don’t need access to the old email address in order to change your Apple ID. This is preferable if you have old purchases or other information you wish to keep.* From Apple ID FAQ:


  I no longer have an email address that was also my Apple ID. Can I still use the email address as my Apple ID?
  
  Apple recommends you change your Apple ID to your current, working email address. This will not create another Apple ID, it will only
  change it to your working email address. See Changing the name you use
  for your Apple ID if you'd like more information.


*It’s important to note that you cannot merge Apple IDs. Period (period).