Why didn't

another agent take the 007 code after Bond retired / quit some many previous times before?

Skyfall - Bond is thought to be dead, MI6 cleared out his flat, sold all his shit. Bond comes back to service and is still 007.
Die Another Day - Bond is imprisoned in N. Korea for years, not sure if he is even alive. Bond comes back to service and is still 007.
License to Kill - Bond resigns from MI6. Still referred to as 007 throughout the movie by Q. If Dalton's 3rd movie had been made he would be 007.

James Bond is 007, 007 is James Bond, they are synonymous.