Yes, it's Gauss. In fact the technique is sometimes known as "Gaussian summation". The New Scientist has an article where the author chases down early references to the story: https://www.americanscientist.org/article/gausss-day-of-reck...

The earliest reference is a biography of Gauss published a year after his death by a professor at Gauss' own university (Gottingen). The professor claims that the story was "often related in old age with amusement and relish" by Gauss. However, it describes the problem simply as "the summing of an arithmetic series", without mention of specific numbers (like 1-100). Also, it was posed to the entire classroom - presumably as a way to keep them busy for a couple of hours - rather than as an attempt to humiliate a precocious individual.