From what I researched a few years ago, you are correct that Fiat/Chrysler owns the Kaiser Frazer name. The name followed the various corporate sales history of Kaiser Corp. as follows, in general:
Kaiser Frazer buys Willys becomes Kaiser Willys Corp. Becomes Kaiser Jeep Corp. bought by American Motors then Bought by Chrysler then bought by Fiat. All corporate trademarks and patents followed the sale.
As an aside Graham Paige didn't disappear either. After it sold it's production facilities and equipment to Kaiser it became a Real Estate company and actually owns Madison Square Garden in New York if you dig through the corporate soup.
