According to the Encyclopedia of Arda, the Beornings were:
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The descendants of Beorn, who dwelt in the Vales of Anduin between Mirkwood and the Great River, and who for many generations retained their ancestor's ability to take the shape of a bear.
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Just because Beorn was the only shape-shifter mentioned in the Hobbit doesn't mean that there weren't any others. It could be like saying there were no Dwarf women, because none were mentioned there (except for Dis, the mother of Fili and Kili, and the sister of Thorin, but she's an exception).