Charles Richter never called it the Richter scale. Someone else named it for him, and colleagues argued about the credit for decades.
The problem it solved was practical. Harry Wood founded Caltech's Seismological Laboratory in 1921, and his team built seismographs to record local Southern California quakes. Richter was hired to analyze the data, a job he first saw as temporary. At the time, earthquakes were usually ranked by the Mercalli scale, which was based on what people felt and what was damaged. Richter and Wood wanted a measurement taken from the instruments themselves.
The key idea came from Beno Gutenberg, who joined Caltech in 1930. Earthquake sizes ranged so widely that no simple scale could hold them, so Gutenberg suggested a logarithmic one. Richter later wrote that "the scale fell right out of my hands." Each whole step means ten times the swing on a seismograph. In energy, Wikipedia says, one step is about 31.6 times more.
Richter published the method in 1935, in a paper titled "An Instrumental Earthquake Magnitude Scale." Accounts differ on the word "magnitude." Wikipedia says Richter used it at Wood's suggestion. History.com says Richter borrowed it from astronomy, where star brightness is rated in magnitudes on a similar logarithmic idea.
The name came from the press. History.com reports that when a reporter asked Berkeley seismologist Perry Byerly what to call the new scale, he answered, "Call it the Richter scale." Merriam-Webster dates "Richter scale" in English to 1936.
That left Gutenberg out of the name. Britannica says the scale was devised by both Richter and Gutenberg. Physics World, reviewing a biography by Susan Hough, says many seismologists hold that the right name is "Gutenberg-Richter scale." Hough writes that Richter felt "a unique sense of ownership" of his scale. Still, History.com says he never denied the roles of Gutenberg and Wood, and that Gutenberg's children led efforts to rename it.
The scale itself has since been retired. Wikipedia says it was defined for Southern California conditions and one standard seismograph, which saturated in strong quakes. In the 1970s it was replaced by the moment magnitude scale. News reports still often call those numbers "Richter," so the name has outlasted the method.