Try this, it will works.
protected void gv1_RowUpdating(object sender, GridViewUpdateEventArgs e)
{
GridViewRow gvRow = gv1.Rows[e.RowIndex];
string Name = ((TextBox) gvRow.Cells[1].Controls[0]).Text;
}
Or
protected void gv1_RowUpdating(object sender, GridViewUpdateEventArgs e)
{
string Name = ((TextBox) gv1.Rows[e.RowIndex].Cells[1].Controls[0]).Text;
}