Should functions preserve their name and length properties (and thus their reflective ability)?

As a functional programmer I regularly pass functions to higher order functions, to combine them in a specific way and create new behavior. Often HOFs serve as wrappers that – as a side effect - disguise the original properties of the given function, a curry function for instance.

I wonder if this reflective ability of functions should be preserved throughout the code, although this may result in considerable costs. Or is it poor style to build dependencies against such properties anyway?

If you think that this question is mainly opinion based, just answer the following:

Are there any use cases that rely on length or name in order to be implemented at all/effectively?