In casting about for ideas for a new comic book character someone at Harvey Comics decided a man wrongfully convicted of murder would be a good candidate to join the costumed hero ranks. In 1941 his origin was presented in Pocket Comics #1, and I’m showing it to you thanks to the folks at Heritage Auctions who scanned it. You can see the Zebra was a prisoner framed for murder who escaped two days short of his execution date, and set about to clear his name.
Huh. Well, if we accept that then we can accept that his costume, derived from his prison garb, gave him his name.
My usual source for credits, the Grand Comics Database, has no information on the artist for this story. Later the Zebra was put in the hands of artist Bob Fujitani. The costume was modified (stripes on shirt only), as shown in an April posting, Pappy's #1354.