We investigate the dynamics of Bose-Einstein-condensate droplets composed of ${}^{164}\mathrm{Dy}$ atoms formed in a double-well potential following removal of the interwell barrier. By solving the dipolar Gross-Pitaevskii equation, we determine phase diagrams of ground-state configurations as functions of the number of atoms confined in the double-well potential. For an interwell separation $2d=3\mu \mathrm{m}$, we consider the relative dipolar-to-contact interaction strengths ${\varepsilon }_{dd}=1.4$, 1.45, and 1.5. Symmetry-broken lowest-energy configurations are found for ${\varepsilon }_{dd}=1.5$ and, over a reduced range of numbers of atoms, for ${\varepsilon }_{dd}=1.45$, whereas no symmetry-broken states are found for ${\varepsilon }_{dd}=1.4$ up to $N=5\times {10}^4$. We analyze the subsequent time evolution after removal of the central barrier, revealing both droplet oscillations and merger events leading to the formation of larger droplets. The oscillations are driven by the external potential and by the repulsive tails of the in-plane component of the dipolar interaction. For the two-droplet states at ${\varepsilon }_{dd}=1.5$ and $2d=3\mu \mathrm{m}$, merging is found for $N=8000$ and 8800, whereas the droplets remain separated for the investigated cases with $N\ge 9000$. Increasing the initial separation to $2d=5\mu \mathrm{m}$ shifts the approximate upper number of atoms for merging to $N\simeq 1.65\times {10}^4$, demonstrating that the crossover is controlled by the competition between the postquench excess energy and the repulsive interdroplet barrier.

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• Spinor Bose-Einstein condensates
• Bose-Einstein condensates
• Dynamical mean field theory