Add a "Net Port Mode" selection to the Schematic Editor that would allow a user-defined Net Port behavior. For example, when connecting a Net Port to a new net/wire...
1) The "Rename Net Port" option forces the Net Port to disconnect from all other identically-named Net Ports, then gives it the same name as the wire's net and finally connects it to the wire. This would eliminate unintended and unreported connections between different nets.
2) The "Rename Wire/Net" option would retain the current behavior of connecting the wire to the same net as other identically-named Net Ports.
The following is an example of what the menu might look like...