Named Entity Recognition (NER) is a fundamental NLP task, commonly formulated as classification over a sequence of tokens. Morphologically-Rich Languages (MRLs) pose a challenge to this basic formulation, as the boundaries of Named Entities do not necessarily coincide with token boundaries, rather, they respect morphological boundaries. To address NER in MRLs we then need to answer two fundamental questions, namely, what are the basic units to be labeled, and how can these units be detected and classified in realistic settings, i.e., where no gold morphology is available. We empirically investigate these questions on a novel NER benchmark, with parallel token-level and morpheme-level NER annotations, which we develop for Modern Hebrew, a morphologically rich-and-ambiguous language. Our results show that explicitly modeling morphological boundaries leads to improved NER performance, and that a novel hybrid architecture, in which NER precedes and prunes morphological decomposition, greatly outperforms the standard pipeline, where morphological decomposition strictly precedes NER, setting a new performance bar for both Hebrew NER and Hebrew morphological decomposition tasks.