It's partly (almost) true, Spicerack. When Swallow Coachbuilding Company teamed up with Standard Motor Company and put Standard engines in to their chassis they named the model SS1 (Swallow + Standard). This happened in 1932.
After some convuluted business changes the company then became SS Cars Ltd who bought out Swallow Coachbuilding and wound it up.
The Swallow name ceased to exist in 1934. Like a phoenix it rose from the ashes in 1935 purely to make sidecars and was in no way connected with SS Cars.
So now we have a brand new public company, SS Cars Ltd who made cars they called SS Jaguar. In 1945 they changed the name to Jaguar