Why can I not designate a library

Are you asking about the Photos preference "Use as System Photo Library"?

If this option is grayed out, the library you are currently viewing is already your System Photo Library. If it looks like this, all is well:

You may want to check the first line in the panel with the "Library Path". Does it show the path to the library you want to be using?

If that is not the problem, please explain in more detail, what you are trying to do and where it is not working as expected.

To switch between several photo libraries and to use them in turn, it should suffice to double click the library you want to open in Photos.