As for the spherical shape, the term there is hydrostatic equilibrium: https://en.wikipedia.org/wiki/Hydrostatic_equilibrium.
Keep in mind it's not actually possible to just "capture" an asteroid. The object needs to lose speed somehow in order to be captured.
Most likely via collision - something large hitting the planet, or two other moons crashing.
So the story of the moons is much more complicated than just "random piece of rock".
As for the spherical shape, the term there is hydrostatic equilibrium: https://en.wikipedia.org/wiki/Hydrostatic_equilibrium.