I'm writing a story related to 'symmetry' and would like to detonate an asymmetric moon. Would gravity allow this? Could a moon be any other shape but round?
Of course it can. You need not look further than out next neighbour outwards. The moons Phobos and Deimos of Mars are distinctly asymmetrical:
All that is required is that it is not massive enough to be formed into a globe by its own gravity, the so called hydrostatic equilibrium.