// Make sure to reference the event handling code

this.tabMyTabControl.SelectedIndexChanged +=
    new System.EventHandler(this.tabMyTabControl_SelectedIndexChanged);

....

private void tabMyTabControl_SelectedIndexChanged(object sender, EventArgs e)
{
    // Use this cast to get a reference to the parent TabControl
    // or simply reference the control directly

    TabControl tc = (TabControl)sender;
    string s = tc.Name;

    // Method 1.
    // Use the SelectedIndex property to get a reference to
    // the TabPage using the TabPages collection
    // You should check that SelctedIndex is not -1!

    TabPage tp = tc.TabPages[tc.SelectedIndex];
    s = tp.Name;
   
    // Method 2
    // Use the SelectedTab property to get a reference to
    // the current TabPage
    // I also illustrate how to access the TabControl directly,
    // rather than using a cast of the sender argument

    tp = this.tabMyTabControl.SelectedTab;
    s = tp.Name;
}