Terahertz (THz) communications has emerged as a promising technology for future wireless systems due to its potential to support extremely high data rates. However, severe path loss, blockage effects, and sensitivity to beam misalignment pose major challenges to reliable indoor THz communications. In this paper, we investigate the coverage probability of downlink transmission in a three-dimensional (3D) indoor THz communication system under structured access point (AP) deployments, with a focus on square and hexagonal grid topologies. A tractable analytical framework is developed to jointly account for human blockages, correlated wall blockages across APs, beam training, and residual pointing error. Numerical results demonstrate that wall blockage correlation significantly reduces the association and coverage probabilities, and its impact cannot be neglected in system performance analysis. Compared with square grid AP deployments, hexagonal grids consistently achieve higher coverage by mitigating correlated wall blockage effects and reducing the distances between user equipments (UEs) and their associated APs. Furthermore, coverage performance is shown to strongly depend on the UE location, with noticeable degradation as the UE moves away from its nearest AP. Residual pointing error is found to introduce substantial coverage loss, especially for longer links. In addition, beam training analysis reveals a non-monotonic relationship between antenna array size and training overhead, highlighting an inherent tradeoff among antenna configuration, beamwidth selection, and beam training efficiency. These findings provide useful insights into the design and deployment of practical indoor THz communication systems.