Extremely large-scale antenna array (ELAA) is a key candidate technology for the sixth generation (6G) mobile networks. Nevertheless, using substantial numbers of antennas to transmit high-frequency signals in ELAA systems significantly exacerbates the near-field effect. Unfortunately, traditional hybrid beamforming schemes are highly vulnerable to ELAA near-field communications. To effectively mitigate severe near-field effect, we propose a novel dynamic hybrid beamforming architecture for ELAA systems, in which each antenna is either adaptively connected to one radio frequency (RF) chain for signal transmission or deactivated for power saving. For the case that instantaneous channel state information (CSI) is available during each channel coherence time, a real-time dynamic hybrid beamforming design is developed to maximize the achievable sum rate under the constraints of the constant modulus of phase-shifters (PSs), non-overlapping dynamic connection network and total transmit power. When instantaneous CSI cannot be easily obtained in real-time, we propose a two-timescale dynamic hybrid beamforming design, which optimizes analog beamformer in long-timescale and digital beamformer in short-timescale, with the goal of maximizing ergodic sum-rate under the same constraints. Simulation results demonstrate the advantages of the proposed dynamic hybrid beamforming architecture and the effectiveness of the developed algorithms for ELAA near-field communications.