In terms of the upcoming election, I think this discussion is all moot. The Trump campaign and the Republican party are going to label the Democratic nominee as a socialist, no matter if that is Bernie or Klobuchar or whoever. The specific language may change, but not the emphasis or frequency. So avoiding the self-labeled "democratic socialist" isn't going to buy you anything on that front. Possibly - although I think unlikely - Bernie's owning of the label may allow him to perform some useful ju-jitsu whereas Amy or someone else could only deny, deny, deny.