k-means clustered data: how to label newly incoming data

This is not answerable without knowing something about the data itself and where it comes from and what it means. But it sounds like you're trying to do something awfully dubious. It sounds like you're trying to come up with labels for free, with a purely automated method. You'll need to obtain labels from some ground-truth source of data (e.g., human labelling; retrospective analysis); no amount of pure algorithms can replace that. See Efficiently labelling training data in machine learning.