How to choose the characteristic length in Reynolds number formula?

The length in the Reynolds number is just a "characteristic length". Certainly the actual dynamics of the system can depend on the shape of the object, but the Reynolds number is "derived" from certain defined scales, so the shape is not important for this specific number.

A description from Wikipedia might help:

This dimension is a matter of convention – for example radius and diameter are equally valid to describe spheres or circles, but one is chosen by convention. For aircraft or ships, the length or width can be used. For flow in a pipe, or for a sphere moving in a fluid, the internal diameter is generally used today. Other shapes such as rectangular pipes or non-spherical objects have an equivalent diameter defined.

Essentially, the choice of the length parameter just effects how your fluid dynamics equations are non-dimensionalized. As long as you understand which lengths are used where, then you know how to compare Reynolds numbers for different systems to understand how similar/different the resulting dynamics might be.