In order to clone a git repository one must have the name of the repository. When working with many repositories it can be hard to remember all the different names, so now I'm wondering if there is possible to list all existing repositories on the remote server using some git command.
You'd either need Shell access to the machine hosting the git-daemon and see the params used to invoke git-daemon or use the Git Web frontend (Repository browser) called GitWeb.
Also refer this existing question
Details are explained in the GitWeb README - the config key of interest is called "GITWEB_PROJECTROOT":
Maybe you could have a talk with you admins - gitweb can be a great profit for all developers.