Monitoring is a default systems profile which is created with the server installation so you can use the same profile to configure your environment.
Self-Monitoring is to check the health status of DynaTrace Server. You can have a looking on the following link for more information.
Apologies for me last answer.
You can remove the 'Monitoring' system profile in the client 'DEBUG' mode (Ctrl + Shift + F9) but I believe there is no harm if it keeps sitting there, otherwise simply disable it if you really don't like :).