Since you are using the SELECT CommandField then you can have something like this

Page2.Aspx 

 protected void Button1_Click(object sender, EventArgs e)
    {
      
        for (int i = 0; i < GrdiView1.Rows.Count; i++)
        {
            if (GrdiView1.SelectedIndex == i)
            {
                String name =GridView1.Rows[i].Cells[1].Text; //Gets the data value in the grid;
                Session["Value"] = name;
                Response.Redirect("Page1.aspx");

            }
        }
       
    }

Page1.aspx

    protected void Page_Load(object sender, EventArgs e)
    {
        string RowValue = Session["Value"].ToString();

         TextBox1.Text = RowValue;
    
    }