FYI for everyone: this issue was due to an old LsPush version being used to scan the machines.
Update your Lansweeper installations if necessary and make sure that your group policies/scripts/tasks are using the latest LsPush executable, which can be found in the Program Files (x86)\Lansweeper\Client folder on your Lansweeper server when you've updated.
Old LsPush versions could only detect the currently logged on user if run under that user. If you ran LsPush as a scheduled task (which, by default, does not run under the currently logged on user), computername$ would be returned as the currently logged on user. This issue was fixed in newer LsPush releases, which can detect the currently logged on user even when run as a scheduled task.