This sounds suspiciously like an urban myth to me – a bit like the one about Otto Titzling and Phillippe de Brassiere. But it is given some credence on the website about.com (which, however, doesn't actually name the two German inventors).
Messrs. Pohlig and Gottschall are credited on Wikipedia, but with only only one citation – and it's in German.
Wikipedia also says that 'A spring stilt utilizing compression springs on each foot was patented in 1891 by George H. Herrington of Wichita, Kansas "for leaping great distances and heights"'. It goes on to say that "The two-handle pogo stick design was patented by George B. Hansburg in 1957." So even if Pohlig and Gottschall did exist, they're only part of the story. (Note also that according to about.com, Mr. Hansburg patented his design in 1919 and not 1957.)
Wikipedia provides a link to a YouTube clip, in which Mr. Hansburg appears on the television programme What's My Line. Not surprisingly, the panel fails to work out that he is the inventor and manufacturer of pogo sticks. In the clip, Mr. Hansburg gives his explanation for the origin of the name 'pogo'. Frankly, I'd rather believe the Pohlig/Gottchall story; even if they never existed, this is the sort of thing that sticks in your mind – and if it isn't true, you wish it was.
If you don't want to sit through the YouTube clip (it's 8 minutes long), Wikipedia provides a summary of Mr. Hansburg's story.
© Haydn Thompson 2017