Two of those things are not named after a person, and none of them are understandable without special training. Naming something after a person doesn't make it any harder to understand unless there are multiple things named after that person and you can't figure out which they mean from the context.
In case you're wondering about those structures, here is what Wikipedia has to say about them:
- A Riemannian manifold "is a real, smooth manifold, M, equipped with a positive-definite inner product g_p on the tangent space T_p M at each point p."
- "A complex manifold is a manifold with an atlas of charts to the open unit disk in C^n, such that the transition maps are holomorphic."
- "A symplectic manifold is a smooth manifold, M, equipped with a closed nondegenerate differential 2-form ω, called the symplectic form."
The only thing in the above descriptions accessible to non-specialists is probably that the Riemannian manifold is probably named after that guy that they heard of in calculus class. Let's not get rid of our ability to honor people in a failed attempt to make the communication more effective. You can call a Riemannian manifold or a Kähler manifold whatever you want, but it's not going to prevent someone from having to spend years before they are able to understand them.