How to save checked status for checkbox in data grid view c# windows application

I am working in c# windows application populate record from sql server to data grid view, with dynamic checkbox facility in each row. i want to select selected rows for some purpose via checkbox of that particular row. till now i successfully achieve my target. but i'm facing a minor issue regarding saving a checked status, Example i want to check only those records whose Name = Max i have a textbox in that textbox i call text chnage event with like Query

Code for Filter by name:

 try
        {
            SqlCommand cmd = null;
            SqlConnection con = null; Ranks rank = new Ranks();
            con = new SqlConnection(cs.DBcon);
            con.Open();
            cmd = con.CreateCommand();
            cmd.CommandText = "Select * from Records where Name like @Name order by Pno";
            cmd.Parameters.AddWithValue("@Name", "%" + FilterByNameTextbox.Text.Trim() + "%");
            SqlDataAdapter adapter1 = new SqlDataAdapter(cmd);
            DataTable dt = new DataTable();
            adapter1.Fill(dt);

            dataGridView1.DataSource = dt;
            Make_fields_Colorful();
        }
        catch (Exception exception)
        {
            MessageBox.Show(exception.Message, "Error", MessageBoxButtons.OK, MessageBoxIcon.Hand);
        }

if i write Max in filter by name textbox it would return 3 records with name starts with max using like query as i mention code above. so i only check 2 records out of 3 using dynamic checkbox, till now my code runs perfectly. Now i want to check records which name starts from Ali, now when i write ali in my filter by name textbox it will return rows where name like ali , but problem comes here it will remove my previous checked records, so how i would able to save checked records for both max and ali's rows:

Code for adding dynamic checkboxes in each row

   DataGridViewCheckBoxColumn checkBoxColumn = new DataGridViewCheckBoxColumn();
        checkBoxColumn.Name = "checkBoxColumn";
        checkBoxColumn.DataPropertyName = "Report";
        checkBoxColumn.HeaderText = "Report";
        dataGridView1.Columns.Insert(10, checkBoxColumn);
        dataGridView1.RowTemplate.Height = 100;
        dataGridView1.Columns[10].Width = 50;

Please suggest me with your code , i would like to appreciate your quick response.

Thanks in advance