The hole came first, and the name followed it.
In 1912 Clarence Crane, a Cleveland chocolate maker born in Garrettsville, Ohio, had a summer problem. Chocolate sales dropped in hot weather because the chocolate melted. So he began testing hard candy that could survive the heat.
The idea for the shape came from a pharmacy. Crane saw a machine that pressed round, flat pills. Mints at the time were mostly square, and most were imported. A round mint would stand out, and the same machine could punch a hole through the center.
With the hole, each mint looked like a tiny ring life preserver, the kind used on boats. Such rings were also called "life savers." That gave Crane his brand name. His first and only flavor was Pep-O-Mint, sold with the slogan "For that stormy breath."
The word was already old. Etymonline records life-saver in English from 1883, for a person or thing that saves lives. Its figurative sense dates from 1909. Etymonline then notes the 1912 candy brand, named for its shape.
A popular story says Crane added the hole after a child choked on a mint. Mental Floss calls that story false. It says Crane wanted his mints to stand apart from the imported European ones, and the name came from the resemblance.
Crane did not keep his creation for long. In 1913 he sold the formula to Edward Noble and his partner J. Roy Allen for $2,900. Cardboard rolls sold poorly, so Noble switched to tinfoil wrappers to keep the mints fresh. Aluminum foil replaced tinfoil in 1925.
The brand then passed through many owners. They included Beech-Nut, Squibb, Nabisco, Kraft and Wrigley, and since 2008 Mars, which bought Wrigley.
Crane's son was the poet Hart Crane. He died at sea in 1932. Mental Floss notes that his death has nothing to do with the candy's design.