Unlike pxSystemNodeID value, the System Name is not autogenerated by PRPC. So, the answer to your question would be "No". The name of current System is dictated by the following Dynamic System Setting value -
If you have observed the System Name got changed after a restart, it is most likely that your Pega server administrator have manually changed the value.
You can inspect the same by opening the DSS (prconfig/identification/systemName/default) and inspecting the "History" tab to see who and when tchanged he System name.