Where should i place my new library?
Further reading: Library management in KiCad version 5
This depends on your personal preference. KiCad does not care where you place your libs as long as your operating system allows you to write to the selected location.
If the library will be used to store project specific footprints then it makes sense to place the library file somewhere under the project directory.
All other libs are best collected into a single directory that is somewhere in your users home directory. (This allows easy backup and sharing of your libraries.)
What should i name my library?
The library name should be unique within the chosen library table. It should also communicate what footpirnts to expect within it to your target audience. Do not include special chars inside your library name as it might create problems in some platforms.
This means the most shareable name will only contain letters, numbers, underline and minus. (This is only a suggestion. Add additional chars at your own risk.)
Selecting the library table
After creating the library you will need to add the library to the global or project library table. Adding it to the global table will make this lib visible to all your projects. The project (also known as local) library table only adds it to the current project.