The terminology adopted for this was "Uralic" for the entire family, "Finno-Ugric" for the non-Samoyedic languages (though "Finno-Ugric" has, to this day, remained in use also as a synonym for the whole family). Finno-Ugric and Samoyedic are listed in ISO 639-5 as primary branches of Uralic. More @Wikipedia
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