The code names do not originate with the Secret Service, but are designated by the White House Military Office.
A source familiar with the process confirms that Carson's code name will be "Eli" and Donald Trump's will be "Mogul."
Trump is expected to get his detail sometime tomorrow.
The Department of Homeland Security received official requests for Secret Service protection from both Carson and Trump in October, and the protection was approved for both campaigns in early November.
Candidates who are front-runners typically request protection around this time of year. Hillary Clinton is the only Democratic presidential candidate with Secret Service protection.