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Quantum spin liquids (QSL) are exotic states that host fractionalized excitations, such as magnetic monopoles, spinons, and anyons. Such QSL states naturally arise in frustrated magnetic systems, such as the J1-J2 Heisenberg model on the triangular lattice. However, smoking-gun signals for quantum spin liquid states are still difficult to identify, both theoretically and experimentally. In this work, we look at the J1-J2 Heisenberg model and calculate the dynamical structure factor, the quantity relevant for neutron scattering experiments, using state of the art matrix product state simulations. We identify experimentally relevant signatures in the low-energy spectrum that distinguish the dominant QSL candidates: the gapped Z2, U(1) Dirac, and spinon Fermi surface QSL states. Our results point to a U(1) Dirac spin liquid, and we discuss the implications of our work on prior and future neutron scattering experiments in triangular lattice compounds.