connect(button1, SIGNAL(clicked()), this, SLOT(markClicked(button1)));

void MainWindow::markClicked(QPushButton *button) { button->setText("Clicked"); }

QSignalMapper mapper;
...
connect(button1, SIGNAL(clicked()), &mapper, SLOT(map()));
mapper.setMapping(button1, button1); // not sure whether this is mandatory or not
...
connect(&mapper, SIGNAL(mapped(QWidget*)), this, SLOT(markClicked(QWidget*)));

void MainWindow::markClicked(QWidget *widget) {
  QPushButton *button = qobject_cast<QPushButton*>(widget);
  button->setText("Clicked");
}