Handle the Click event, and get it's Name property:
private void MyTextBox_Click(object sender, EventArgs e)
{
TextBox tb = sender as TextBox;
if (tb != null)
{
Console.WriteLine(tb.Name);
}
}
Or if you have C#7:
private void MyTextBox_Click(object sender, EventArgs e)
{
if (sender is TextBox tb)
{
Console.WriteLine(tb.Name);
}
}