Heavens no, AMC was not a merger of Studebaker and Packard, although there was a merger of Studebaker and Packard in the fifties. Studebaker would go on to make some great designs, like the Hawks and the Avanti.
AMC was Rambler, a company with roots going back to the early auto industry as the Thomas B Jeffery Co., with a new name. They made some great cars, like the Javelin and the AMX as well as some weirdly wonderful ones, like the Gremlin and the Matador coupe. Did you ever see "Argo"? The cars pursuing the 747 down the runway in Tehran are Matador sedans. AMC went on to produce the excellent AWD Eagles, based on the ancient Hornet chassis as well as the attractive Spirit hatchback based upon the same.
Along the way, AMC had also acquired the Jeep brand and improved it greatly. The first modern Cherokee was an AMC design.
In the eighties, Renault took an interest in AMC and various Renault models were offered at AMC dealers, including the Fuego, the R5 (Le Car) and the really awful Alliance.
Chrysler bought the company after Renault got tired of breaking their pick in the US market, if only because they wanted the Jeep brand as well as its product portfolio.