I've got two AVDs with different names and when I launch application in Appium Inspector, pointing in Capabilities to specific AVD, then may also run in second AVD which is reserved for other purpose.
First find the udid of your emulator. To find the device udid, open command prompt and type:
adb devices
It will list the udid of you connected devices.
Then you need to add the udid in DesiredCapabilities
DesiredCapabilities caps = new DesiredCapabilities();
// others caps
caps.setCapability("udid", "your device udid");