It seems, both from your original question and your follow-up questions, that you don't understand how filesystems work.
A "disk" is nothing but a very very long string of zeros and ones. A computer must use a standard method of managing these zeros and ones, called a "filesystem". There are many different types of filesystems on various types of computers -- FAT32, NTFS, EXTFS, ResierFS, and so no. The choice of filesystem is critical to the relationship between the computer accessing the disk and the zeros and ones stored on the disk. If a filesystem is formatted as an EXTFS, but the computer decides for some reason to use ResierFS to manage the disk, it will end in complete data corruption.
Many Unix-based file systems, for example, EXTFS and its derivatives, will logically divide a disk into multiple sections. One section is the "inode table". This area contains the "inodes". Each inode refers to a specific file and will describe, for example, what type of file it is ("normal" file, directory, device, socket, etc), the owner, the permissions, and the section(s) of the "data" portion of the disk where the file's data can be located.
Then there will be a "data" area. For a "normal" file, the file's contents will be stored here. In the case of a directory, what is stored here is a list of filenames (one name for each file contained inside that directory) and the inodes that each of those filenames refers to.
When you want to find a file, you specify it by its "path". The computer starts at the root of the path ("/"), finds the name of the first object in the path ("usr"), and then
- locates its inode
- notices it's a directory
- gets the name of the next object in the path
- finds that object in the directory
until finally it finds an object whose inode indicates "not a directory".
One of us think the file name is stored in the files' meta-data.
Not in most classic Unix filesystems, no. In FAT32 and NTFS, I have no idea.
The others disagrees, we think the filename is somehow stored in the directory
In most classic Unix filesystems, yes.
or the file-system.
Everything is stored in the filesystem.