Hi Maddison,
The error you are encountering is actually quite common and in most cases, miss-used.
First we actually need to know whether you are actually trying to use Arc Map 10.3.1 with Single Use license (ESU123456789 or EVA123456789) or Concurrent use (EFL12345679).
Second, the issue with "Could not connect to an ArcGIS License manager running on host 'Not_Set'" is actually trying to connect with a License server that you may have installed on different machine or another machine. you will need to know the host-machine name or IP address in order to set that. Now this option again, is for the Concurrent use licenses only or when using the EFL licenses.
Third, there should not be an issue when accessing through Mac via Parallel as long as you machine is able to communicate with the License Server: Configure ArcGIS License Manager to work through a firewall—Help | ArcGIS for Desktop.
These resources might help as well:
Could not connect to an ArcGis license manager running on host "Not_Set".
Error: "Not_Set" is an invalid hostname. Please enter a valid hostname.
FAQ: Why is 'Not_Set' listed in the Desktop Administrator License Manager folder?