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Two-dimensional van der Waals crystals and their heterostructures provide an exciting alternative to bulk wide-band-gap semiconductors as hosts of single-photon emitters. Among different layered materials, bright and robust defect-based single-photon emitters have been observed within hexagonal boron nitride, a layered wide-band-gap semiconductor. Despite research efforts to date, the identities of the deep defects responsible for quantum emissions in hexagonal boron nitride remain unknown. In this theoretical work, I demonstrate that the strain-induced changes in emission frequencies depend on (i) the detailed nature of the defect states involved in the optical excitations, and (ii) the rich boron chemistry that results in complex interactions between boron atoms. As each defect shows a distinct response to the strain, it can be used not only to tune emission frequencies but also to identify the quantum emitters in hexagonal boron nitride.