How could I add "compact" view for file manager? I mean small icons and a file names, or even file names alone (no icon).
It is not currently possible for a 3rd party to provide a new view mode in Files - you would have to become an elementary developer and get a PR merged (new developers are welcomed). I did push an experimental branch providing a compact view some years ago but at that time the design team were not too keen on adding a fourth mode especialy given the steady increase in screen size and resolution.
The column view only shows small icons and filenames of course but only one column per folder.
You can edit the setting "io/elementary/files/icon-view/minimum-zoom-level" using dconf-editor or the command line and change it to "smallest". This allows you to decrease the icon size to the smallest available and get 3x the items compared to List view. However, the names then become rather cramped and hard to read.