Most languages translated this word. English kept it in German.
Kindergarten is two German words joined: Kinder, the plural of Kind, "child," and Garten, "garden." Etymonline calls it a metaphoric name meaning "children-garden, garden of children." Kind is related to English kin, and Garten is a cousin of English garden.
The coiner was Friedrich Fröbel (1782 to 1852), a German educator. New World Encyclopedia says he opened a play and activity institute at Bad Blankenburg, in Thuringia, in 1837. Wikipedia dates the renaming to 28 June 1840, and New World Encyclopedia has him first using the word in 1840. The metaphor was meant seriously. Fröbel believed children should grow naturally, supported by parents and teachers, the way a gardener supports plants. The site even had a real garden where the children grew flowers, vegetables, grains and herbs.
Etymonline records the English word in 1852, the year Fröbel died. Its entry notes that a German Catholic priest, Johannes Ronge, set up the first children's garden in England in 1850.
The first American kindergarten is credited to Margarethe Schurz. The Wisconsin Historical Society says she began one in 1856 in her home in Watertown, Wisconsin, for her daughter and four cousins. She had attended Fröbel's lectures as a teenager in Germany. When more families asked to join, she moved the school into a small building on Charles Street. The Society calls it the first kindergarten in America, and the building still stands as a museum.
English could have done what other languages did. Etymonline points out that Danish renamed the institution børnehave and Modern Hebrew calls it gan yeladim, both meaning "garden of children." English simply borrowed the German word whole, so American five-year-olds still go to a garden.
Etymonline also records the respelling kindergarden by 1879, which puts the English word for garden back inside it.