Its called chromodynamics because the interactions are described by the special unitary group of degree 3, which is the same group that describes how we perceive color interactions.
It's just the three dimensional nature of it plus the usual physics practice of giving things cheeky names. The vector space of (visible) colors is not acted symmetrically upon by SU(3); it doesn't transform symmetrically under charge-preserving unitary matrices. A blue strawberry with red leaves would not seem the same to us as a red strawberry with green leaves.