In 6G systems, extremely large-scale antenna arrays operating at terahertz frequencies extend the near-field region to typical user distances from the base station, enabling near-field communication (NFC) with fine spatial resolution through beamfocusing. Existing multiuser NFC systems predominantly employ linear precoding techniques such as zero-forcing (ZF), which suffer from performance degradation due to the high transmit power required to suppress interference. This paper proposes a nonlinear precoding framework based on Dirty Paper Coding (DPC), which pre-cancels known interference to maximize the sum-rate performance. We formulate and solve the corresponding sum-rate maximization problems, deriving optimal power allocation strategies for both DPC and ZF schemes. Extensive simulations demonstrate that DPC achieves substantial sum-rate gains over ZF across various near-field configurations, with the most pronounced improvements observed for closely spaced users.