Hello,

I am adding little elaborative answer, I have pasted below code you need to write down code on similar lines.

Note: Instead of passing name in payload you can pass it as path parameter. 

(function process(/*RESTAPIRequest*/ request, /*RESTAPIResponse*/ response) {

	var name = request.pathParams.name || null;
	if (!name)
		return new sn_ws_err.BadRequestError("Change Request id not provided");
	
	var result = {};

	var record = new GlideRecord('x_test');
	if(record.get('name', name)){
		if (!record.deleteRecord())
			return new sn_ws_err.BadRequestError("Change Request not deleted");
		else{
			result.status = 'success';
			response.setStatus(200);
			response.setBody(result);
		}
	}else
		return new sn_ws_err.NotFoundError("Change Request not found");

})(request, response);

Step1: Create a scripted REST API with proper name (e.g. Test Table APIs )

Step 2: Create a DELETE scripted REST Resource  as shown in below screenshot