Perform a project -> Recompile (it's in the menu), then open the Messages window and post a list of the error messages you're getting. I have a feeling that what you're seeing is not necessarily a problem.
Perform a transfer from your schematic to the PCB, Altium will warn you that you have unmatched nets. Just say "no" when Altium wants you to match them (Do you want to match those nets manually). This is Altium's way of telling you: "Either you do it and control it manually or I will and do it automatically". In about every case, the automatic way here is the better one.
You will then get an ECO changelist which basically tells you what changes Altium will perform. It will probably delete the nets with the asterisk and add your nets. Confirm the dialog with "Execute". You should actually get correct net names without having to match any of them manually.
If you want to debug, add a net label to any of your nets, Project -> Recompile -> Watch for errors in the messages window. If none, transfer to PCB, you should now see at least the net you added (the name of the net label).