En mi JTable, después de la actualización, se debe actualizar para mostrar los cambios:

public class RecordTableGUI extends JFrame implements ActionListener {
private String newName;
private JTable table;
private RecordTableModel myModel;
private JButton editButton;

    public RecordTableGUI() {
    myModel = new RecordTableModel();
    table = new JTable(myModel);

    add(new JScrollPane(table), BorderLayout.CENTER);
    add(buttonsPanel(), BorderLayout.SOUTH);

    setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);
    setSize(700, 550);
    setLocation(300, 80);
    setVisible(true);
}

public JPanel buttonsPanel() {
    JPanel bPanel = new JPanel();
    editButton = new JButton("Edit");
    editButton.addActionListener(this);
    bPanel.add(editButton);
    return bPanel;
}

@Override
public void actionPerformed(ActionEvent e) {
        if (table.getSelectedRow() > -1) {
        Object oldName = table.getValueAt(table.getSelectedRow(), 1);

        UpdateGUIDialog updDialog = new UpdateGUIDialog(this,String.valueOf(oldName), this);

        int rowToEdit = table.getSelectedRow();
        int rowToModel = table.convertRowIndexToView(rowToEdit);
        Object nameID = table.getValueAt(table.getSelectedRow(), 0);
        myModel.updateRow(rowToModel, nameID, getNewName());
    } else {
        JOptionPane.showMessageDialog(null, "Select a row");
    }
}
}

Clase modelo:

public class RecordTableModel extends AbstractTableModel {
Connection con;
Statement statement;
ResultSet result;
String dbUrl = "jdbc:mysql://localhost/mydb";
String query = "Select * from mytable";
ArrayList<String> cols = new ArrayList<String>();
ArrayList<ArrayList<String>> data = new ArrayList<ArrayList<String>>();

    public RecordTableModel() {
    try {
        con = DriverManager.getConnection(dbUrl, "root", "2323");
        statement = con.createStatement();
        result = statement.executeQuery(query);

        int c = result.getMetaData().getColumnCount();
        for (int i = 1; i <= c; i++) {
            cols.add(result.getMetaData().getColumnName(i));
        }

        while (result.next()) {

            ArrayList<String> eachRow = new ArrayList<String>();
            for (int i = 1; i <= c; i++) {
                eachRow.add(result.getString(i));
            }
            data.add(eachRow);
        }

    } catch (SQLException sqle) {
        sqle.printStackTrace();
    } finally {
        try {
            if (con != null) {
                con.close();
            }
            if (statement != null) {
                statement.close();
            }
        } catch (SQLException sqlee) {
            sqlee.printStackTrace();
        }
    }
}
    @Override
public int getRowCount() {
    return data.size();
}

@Override
public int getColumnCount() {
    return cols.size();
}

@Override
public Object getValueAt(int rowIndex, int columnIndex) {
    ArrayList<String> selectedRow = data.get(rowIndex);
    return selectedRow.get(columnIndex);
}

@Override
public String getColumnName(int col) {
    return cols.get(col);
}
    public void updateRow(int modelRow, Object nameID, Object newName) {
        String query = "update mytable set name = '" + newName + "' where id = " + nameID;
    Connection conn;
    PreparedStatement pstate;
    try {
        conn = DriverManager.getConnection(dbUrl, "root", "2323");
        pstate = conn.prepareStatement(query);
        pstate.executeUpdate();
        fireTableRowsUpdated(tableRow, tableRow);
        fireTableDataChanged();
        fireTableCellUpdated(modelRow, 1);
    } catch (SQLException sql) {
        sql.printStackTrace();
    }
}