Beam alignment is essential to compensate for the high path loss in the millimeter-wave (mmWave) Unmanned Aerial Vehicle (UAV) network. The integrated sensing and communication (ISAC) technology has been envisioned as a promising solution to enable efficient beam alignment in the dynamic UAV network. However, since the digital identity (D-ID) is not contained in the reflected echoes, the conventional ISAC solution has to either periodically feed back the D-ID to distinguish beams for multi-UAVs or suffer the beam errors induced by the separation of D-ID and physical identity (P-ID). This paper presents a novel dual identity association (DIA)-based ISAC approach, the first solution that enables specific, fast, and accurate beamforming towards multiple UAVs. In particular, the P-IDs extracted from echo signals are distinguished dynamically by calculating the feature similarity according to their prevalence, and thus the DIA is accurately achieved. We also present the extended Kalman filtering scheme to track and predict P-IDs, and the specific beam is thereby effectively aligned toward the intended UAVs in dynamic networks. Numerical results show that the proposed DIA-based ISAC solution significantly outperforms the conventional methods in association accuracy and communication performance.