Final answer:
The process mentioned is called 'Breaking the Flag', which signifies the start of a ship's voyage. 'Colors Ceremony' is a related concept, involving the ceremonial raising and lowering of a flag, typically at sunset.
Step-by-step explanation:
The process of moving the flag from the stern to the mainmast as the ship gets underway is called Breaking the Flag. When a ship is about to set sail, this ceremony is symbolic and traditionally marks the beginning of a voyage. Colors Ceremony, on the other hand, is a term generally used to describe the raising and lowering of a flag on a naval vessel at specific times. The phrase "Flaunt away, flags of all nations! Be duly lowered at sunset!" refers to a maritime tradition akin to the Colors Ceremony, where a ship's flag is ceremonially lowered at sunset.