Can two apps have the same name if spacing is different
You can check the availability of a name of app regardless of its origin, spelling or grammar before even creating the app. Log in to iTunes Connect — Click Manage Your Applications -> Add New App (don't fill in a SKU Number or bundle ID); if the name is already taken, you will get the following errors:


  You must select a Bundle ID.
  The App Name you entered has already been used
  provide a SKU.


Act accordingly based on the errors. But AFAIK, without doing all that, the algorithm segregates the two so you should be safe with a space between it since it considers FatCat as one word, unless someone has already reserved it but has not yet submitted it to the App Store or is not yet live in the App Store.