If you want to search the "Name" column from Grid based on searched text, then first step to get the SQL Server data to DataTable and make sure DataTable is a global object so we can able to access on different methods.
Then write a simple method like that.
private void Fill_Grid_With_Searched_Text()
DataView dv = new DataView(dtSearch);
dv.RowFilter = "cust_Name like '" + txtSearch.Text + "%'";
grvCustomer.DataSource = dv;
dtSearch is actually your DataTable which loaded with SQL Server Records
cust_Name is the Database Column Name
And call this method in TextChange event of Searching Textbox.
This looks a faster way to search. Other way is to query from database every time.