On the Get Button click simply write code to save data to database as shown below.

Namespaces

using System.Data;
using System.Configuration;
using System.Data.SqlClient;

Code

protected void GetTextBoxValues(object sender, EventArgs e)
{
    foreach (TextBox textBox in pnlTextBoxes.Controls.OfType<TextBox>())
    {
        string constr = ConfigurationManager.ConnectionStrings["constr"].ConnectionString;
        using (SqlConnection con = new SqlConnection(constr))
        {
            using (SqlCommand cmd = new SqlCommand("INSERT INTO Names(Name) VALUES(@Name)"))
            {
                cmd.Connection = con;
                cmd.Parameters.AddWithValue("@Name", textBox.Text);
                con.Open();
                cmd.ExecuteNonQuery();
                con.Close();
            }
        }
    }
}