Accurate determination of the neutron skin thickness $\left(\mathrm{\Delta }{R}_{\mathrm{np}}\right)$ in finite nuclei is essential for constraining the density dependence of the nuclear symmetry energy. This work presents a systematic investigation of $\mathrm{\Delta }{R}_{\mathrm{np}}$ for the transuranium berkelium (Bk) isotopes within the framework of the deformed relativistic Hartree-Bogoliubov theory in continuum (DRHBc). The results indicate an overall increase in neutron skin thickness with $N$, which exhibits antikinks at the shell closures $N=184,258$ due to the shell effects. A decomposition of $\mathrm{\Delta }{R}_{\mathrm{np}}$ into volume and surface terms, based on two-parameter Fermi (2pF) fits to angle-averaged DRHBc densities, demonstrates that the volume term dominates as much as $60\%\text{–}70\%$ in most nuclei, consistent with the $65\%$ found in ${}^{208}\mathrm{Pb}$, thereby validating the volume-surface decomposition for deformed nuclei and confirming its correlation with the symmetry energy slope $L$. The surface term prevails only near the proton drip line, where the volume fraction drops below $50\%$ due to the reduced neutron-to-proton ratio. Deformation is found to slightly reduce the central radius $R_c$ but markedly enhance the surface diffuseness $a$, leading to a notable increase in $\mathrm{\Delta }{R}_{\mathrm{np}}$, primarily driven by the surface term. Furthermore, we extend the decomposition to a directional analysis by extracting 2pF parameters along the symmetry axis $(\theta =0^{\circ })$ and perpendicular to it $(\theta ={90}^{\circ })$. In prolate deformed nuclei, a strong directional dependence is observed: although the nucleus is elongated along the symmetry axis, $\mathrm{\Delta }{R}_{\mathrm{np}}$ is significantly larger in the perpendicular direction. This anisotropy is weak for oblate nuclei around the shell closures. The anisotropy of $\mathrm{\Delta }{R}_{\mathrm{np}}$ is attributed mainly to the volume term, which remains the dominant contribution in most nuclei regardless of direction. These findings provide new theoretical insights into the interplay among deformation, the neutron skin thickness, and the symmetry energy, and offer a foundation for future experimental probes of neutron skin anisotropy in heavy-ion collisions.

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• Neutron skin thickness
• Nuclear structure & decays
• Symmetry energy
• A ≥ 220