You would be able to do this better if you try using the value of the textbox in the query itself.
For e.g.
SqlCommand cmd = new SqlCommand("select name from Product where name like @City", conn);
SqlParameter param = new SqlParameter();
param.ParameterName = "@Name";
param.Value = textbox1.text;
cmd.Parameters.Add(param);
reader = cmd.ExecuteReader();
If the reader returns a count of 1 or more, a record with this name already exists.