I fi configure rights in jenkins security config project matrix for users connecte via ldap realm, the user id (cn) showw there in our case is just a number.
Adding new users via uid/login ldap attribute is ok-, but
its very difficult to maintain user base as admin without having name attributes shown for avery user also. At the moment i make a manual ldap lookup via a ldap client to get the persons real name (name, sn) and then be sure i set jenkins access rights for the coorect user.

Ldap config should provide config for ldap attribs which are also shown right behind ldap login id. In our case this could be "first name". THis additional information shall be shown in global project matrix cfg and job's one.