Ref.: Car and Driver Magazine
"It began in the 18th century with a horse-drawn carriage featuring a light body, a folding top, and large wheels. It's arachnid (spider) like appearance - tall wheels (like legs) and a small body - likely earned it name 'Spider Phaeton.' In the 1930's, Italians for some reason took to calling two-seater race cars "spiders." After the war, Italy's Cisitalia and Siata brands launched models named Spiders. In 1953, for reasons known only to itself Siata changed the spelling to 'Spyder.' It's all a bit strange since the Italian language rarely uses the letter 'y' and the word for spider in Italian is ragno.
A year after Siata's new spelling Porsche's American importer, Max Hoffman, suggested the recently debuted Porsche 550 - 1500 RS be rebranded as 'Spyder.' That might not be the definitive answer, but it's certainly something."