Reproduction steps:

1. Create a New Project
2. Create a Script and open it with Visual Studio Code
3. Try to debug

Expected Result: The Debugging process starts
Actual Result: Error appears, "Multiple targets with name 'Unity Editor' running. Unable to connect."

Fixed in: Visual Studio Code Debugger extension ​​v1.3.0​​​​​

Reproduced with: 2018.2.0a1, 2018.1.0b6, 2018.1.0b1, 2018.1.0a7, 2018.1.0a6, 2018.1.0a4, 2018.1.0a3(a20833), 2018.1.0a3(f88474), 2018.1.0a2
Did not reproduce on: 2018.1.0a1, 2017.3.1p1, 2017.2.1p4

Note:
VSC Version 1.19.3

Workaround:
Start "Task Manager" -> Open up the "Unity" process list -> Click on "UnityCrashHandler64" -> "End task"