Coast Guard
Capitalize in U.S. context and when preceded by name of country.
The U.S. Coast Guard is under the U.S. Department of Homeland Security (in wartime, under the Navy Department) and is one of the nation's five armed services.
United States Coast Guard, the Coast Guard
U.S. Coast Guardsman Jones, a Coast Guardsman, the guardsman (OK to use for females, though preference is for gender neutral terms, such as "member")
Other:
Canadian Coast Guard, the coast guard
coast guardsman Smith (OK to use for females, though preference is for gender neutral terms, such as "member")
See also: AIR FORCE, ARMY, MARINE CORPS, NAVY,