We investigate the evolution of clustering structure through the momentum distributions in the $^{8-10}$Be isotopes. The nucleon dynamics within the inter-cluster antisymmetrization are discussed via the momentum distribution of a Brink type $alpha$-$alpha$ wave function. For the state with a small $alpha$-$alpha$ distance, we observe a significant depression with a dip structure at zero-momentum and an enhanced tail at relatively higher momentum region. In addition, we find the cluster structure in the intrinsic frame of momentum space, which is complementary to its significant $alpha$-cluster dissolution in the coordinate space because of the strong antisymmetrization. For the physical $^{8-10}$Be isotopes, the Tohsaki-Horiuchi-Schuck-R{o}pke (THSR) wave functions are adopted. The evolution from the dilute clustering state to the compact one is demonstrated by a successive depression at the zero-momentum of nucleon distribution for the two $alpha$-clusters within $^{8-10}$Be isotopes. For the compact $^{10}$Be nucleus, the momentum distribution of all nucleons shows significant depression at zero-momentum with a dip structure, which is found to be contributed by both the inter-cluster antisymmetrization and the $p$-orbit occupation of the valence neutrons. This study proposes a new window for the investigations of the $alpha$-clustering effects via the low-momentum components of nuclei, which is expected to be extended to the heavier nuclear clustering states.
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