Within the relativistic point-coupling model in conjunction with the similarity renormalization group (SRG), we systematically investigate the correlations between relativistic symmetry and subshell evolution in nuclear systems. Guided by the concepts of pseudospin symmetry (PSS) and spin symmetry (SS), we study the formation of bubble-like structures in both new $N\left(Z\right)=14,16$ and traditional $N=82$ magic number isotones. By analyzing neutron/proton density profiles and the breaking behavior of PSS across the isotopic chain from neutron-rich oxygen (O) to neutron-deficient calcium (Ca), our model identifies all examined $N=14$ isotones as potential neutron bubble nuclei. For proton bubble-like candidates, ${}^{22}\mathrm{O}$ to ${}^{28}\mathrm{Si}$ (in $N=14$ isotones) and ${}^{28}\mathrm{Mg}$ to ${}^{30}\mathrm{Si}$ (in $N=16$ isotones) are proposed. In the light nuclei region, the emergence of semibubble structures is attributed to large pseudospin energy splitting, whereas the formation of bubble-like structures in $N=82$ isotones is unlikely due to small pseudospin energy splitting and the intervening $1h_{11/2}$ orbital between the $3s_{1/2}$ and $2d_{3/2}$ states. Through analytical decomposition of the Dirac Hamiltonian using SRG, we clarify the origins and breaking mechanisms of PSS and SS. A key distinction between light and heavy systems is revealed: in light systems, the spin-orbit term primarily determines the quality of PSS, while in all examined mass regions, SS is governed by spin-orbit interactions. Notably, the dominant role and variation of the spin-orbit term in determining PSS quality in light systems serves as a clear indicator for the emergence or suppression of bubble-like structures.

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• Nuclear structure & decays
• Nucleon distribution
• 20 ≤ A ≤ 38