In this paper, the physical layer security of terahertz (THz) band communications in the near field is discussed and evaluated. First, a novel class of design approaches to enhance the security of near-field THz links is proposed. These approaches are referred to as wavefront hopping schemes, as they exploit the properties of different THz wavefronts when propagating beams in the near field (particularly, THz Bessel beams and THz Airy beams). Then, a compound evaluation framework is delivered to assess both the performance and the security level of a given single-beam or multi-beam solution for a near-field THz system. Finally, a performance evaluation is conducted illustrating the performance/secrecy trade-offs associated with the modeled single-beam and multi-beam security schemes for both a single Attacker and a team of cooperating Attackers. Our results indicate that the proposed multi-beam solutions combining THz Airy beam(s) with THz Bessel beam through wavefront hopping lead to a notably decreased probability of message eavesdropping while maintaining nearly identical performance with the single-beam schemes. The contributed security schemes, evaluation methodology, and numerical results facilitate further development in the emerging area of secure near-field THz communications for 6G and beyond wireless networks.