When a dialog is created using, for instance, Alert#showAndWait() it has an empty icon in the title. it should have the same icon as the application that it is running from. Here is an example code:

public class DialogDemo extends Application {
    @Override
    public void start(Stage primaryStage) throws Exception {

        Image image = new Image("icon.png");
        primaryStage.getIcons().add(image);

        Button button = new Button("Show Dialog");
        button.setOnAction(event -> {
            Alert alert = new Alert(Alert.AlertType.ERROR);
            alert.initOwner(primaryStage);
            alert.setContentText("Message");
            alert.setHeaderText("Header");
            alert.setTitle("Title");
            alert.showAndWait();
        });

        BorderPane root = new BorderPane();
        root.setCenter(button);
        
        Scene scene = new Scene(root, 300, 300);
        primaryStage.setScene(scene);

        primaryStage.show();
    }
}