The Rainsberger name is one of the variations that have developed from the Swiss Rymensperger identified as early as Matthias born circa 1595. The family appears to have come from Buch, Thurgau, Switzerland. The family appears to have migrated to Baden-Wurtenberg, Germany and the name underwent a spelling change to Riemensperger.
John (1759-1850) seems to be the first to use the Rainsberger spelling and most of his descendants have used it. Some have dropped the final er.