Terahertz (THz) communications is envisaged as one of the key enablers for beyond fifth-generation (5G) wireless networks because of its massive bandwidth opportunities. However, wireless transmission at such high frequencies comes with its own challenges, including the increased power consumption and hardware complexity, the challenging task of channel estimation, as well as the strong impact of phase noise (PN). In this work, we consider coherent and noncoherent transmission techniques based on spatial modulation (SM) for the THz channel with PN impairments. SM schemes carry part of the information by the baseband modulated symbols and part by the used antenna or subarray index. Our investigations show that the index detection in the SM chain remains robust against the strong PN impairment, unlike the symbol detection which deteriorates as the modulation order increases. The robustness of index detection under PN coupled with low modulation order renders SM an attractive candidate for THz communications. Under strong PN, space-shift keying (SSK) schemes, i.e., SM schemes which solely transmit index information, are preferable.