The German Wikipedia article on Salzburg (https://de.wikipedia.org/wiki/Salzburg#Namensgebung) has an extensive section on the name. It mentions that salt mining in Hallein only started when Salzburg already had its name, so the name is either connected to Reichenhall or derived from the river Salzach on which it's located. Despite the area being undeniably salty, Salzburg itself didn't have a salt mine or play an important role in the salt trade.