The popular term; DELTA or The Delta Force is no longer used by the US Army or by the DoD/USSOCOM.
The "new" name for SFOD-D is now; ACE or Army Compartmentalized Elements. Not to be confused with ACE(Army Corps of Engineers)
ACE was also called CAG or Combat Applications Group but that was ended about 2 years ago.
I'm sure in time, ACE will be changed too but for now, keep in mind, the Delta Force was disbanded.