The emergence of 6G networks demands endogenous solutions for wireless security and privacy, leveraging advanced techniques like physical-layer security, covert wireless communications, and orthogonal time frequency space (OTFS) to combat evolving threats and enable secure interconnected systems. However, OTFS needs to be reconsidered in low Earth orbit (LEO) satellite covert communications, due to the overspread Doppler squint effect (ODSE) caused by excessive accumulation time combined with high relative velocities. This paper analyses the impact of ODSE affecting more than one grid and proposes an energy-density clustering acquisition (ECA) scheme. By redefining the neighborhood structure and employing a power-centered clustering approach, the ECA scheme enhances detection probability and estimation accuracy while maintaining low computational complexity. Simulation results confirm the performance superiority compared with traditional acquisition schemes.