I'm using Amazon's Echo Dot, and I have several Echo devices. I want to identity that, from which echo dot invokes a request, is it possible to find whether which, echo dot makes request, with any unique identity?
Yes. In the Alexa Skill Kit Documentation is a chapter about Request and Response JSON Reference. If you look here.
Look for the device object in your request. It includes an unique device-ID.
var yourDeviceID = this.event.context.System.device.deviceId;