Zero-shot named entity recognition (NER) is the task of detecting named entities of specific types (such as 'Person' or 'Medicine') without any training examples. Current research increasingly relies on large synthetic datasets, automatically generated to cover tens of thousands of distinct entity types, to train zero-shot NER models. However, in this paper, we find that these synthetic datasets often contain entity types that are semantically highly similar to (or even the same as) those in standard evaluation benchmarks. Because of this overlap, we argue that reported F1 scores for zero-shot NER overestimate the true capabilities of these approaches. Further, we argue that current evaluation setups provide an incomplete picture of zero-shot abilities since they do not quantify the label shift (i.e., the similarity of labels) between training and evaluation datasets. To address these issues, we propose Familiarity, a novel metric that captures both the semantic similarity between entity types in training and evaluation, as well as their frequency in the training data, to provide an estimate of label shift. It allows researchers to contextualize reported zero-shot NER scores when using custom synthetic training datasets. Further, it enables researchers to generate evaluation setups of various transfer difficulties for fine-grained analysis of zero-shot NER.