OleDbConnection oleCon = new OleDbConnection(excelConnectionString);
oleCon.Open();
var query = string.Format("SELECT * FROM [{0}$]", worksheetName);
using (var cmd = new OleDbCommand(query, oleCon))
{
    using (var da = new OleDbDataAdapter(cmd))
    {
        da.Fill(ds, worksheetName);
    }
}

using (var con = new SqlConnection(sqlConnectionString))
{
	con.Open();
	using (var insertCmd = con.CreateCommand())
	{
		insertCmd.CommandText = "INSERT INTO Names (Number, Name) VALUES (@Number, @Name)";
		insertCmd.Parameters.Add("Number", SqlDbType.NVarChar, 100, "Номер договора");
		insertCmd.Parameters.Add("Name", SqlDbType.NVarChar, 100, "Клиент");
		using (var adapter = new SqlDataAdapter())
		{
			adapter.InsertCommand = insertCmd;
			adapter.Update(ds, worksheetName);
		}
	}
	con.Close();
}

OleDbConnection oleCon = new OleDbConnection(excelConnectionString);
oleCon.Open();
var query = string.Format("SELECT * FROM [{0}$]", worksheetName);
using (var cmd = new OleDbCommand(query, oleCon))
{
    using (var da = new OleDbDataAdapter(cmd))
    {
        da.AcceptChangesDuringFill = false; // <-- не хватало вот этого
        da.Fill(ds, worksheetName);
    }
}