During WWII, the Navy and all other branches followed a practice that had been established during the First World War (which lapsed during peacetime). This practice was that the U.S. Army became the lead agency for the reporting of all American casualties. The Army's Casualty Branch and Graves Registration Service (GRS) was given all records on all military personnel, so they could handle this task efficiently.
At the beginning of WWII, casualty reports from the battle theater to Washington were made by radiogram or cable. The error rate using this system reached 25% by 1943, so a new system was put in place. This was a punchcard method. Cards were made by the Machine Records Unit servicing the Army. Then they were checked by theater headquarters, and dispatched to the War Department by air officer courier. Casualty reports were automatically done by machine from the punchcards.
After this came the official notification to the family. The completed casualty reports were the basis from which telegrams were formulated and sent. They did not contain many of the details that families wished to receive, but were completely automated forms to ensure speedy notification. These initial telegrams were the same without regard to rank. They only differed in type (wounded, captured, killed).
On Oct. 3, 1944, theater commanders were directed to send personal letters of condolence which included individual details, for each and every soldier's death. These were sent by air mail direct. These letters were written by designated unit or hospital personnel or chaplains, and a copy of each letter was to be sent to the Casualty Branch.
You can learn more about the details of how the Navy handled casualties by going to: http://www.archives.gov/publications/ref-info-papers/82/introduction.html I summarized the main points, but details about the Navy are near the end of this report.