Excel相互運用機能を使用すると、この方法で実行できます。関数名はExcelブックで定義されている関数を指していると思います。そうでない場合は、リフレクションを使用するようにその部分を変更する必要があります(ただし、この場合、メソッドのレシーバーが必要ですが、1つは表示されません。質問で)。
object hmissing = System.Reflection.Missing.Value;
Xls.Application App = new Xls.ApplicationClass();
App.Visible = true;
Xls.Workbook wb = App.Workbooks.Open(@"c:\tmp\cartel1.xls", hmissing, hmissing, hmissing, hmissing, hmissing, hmissing,
hmissing, hmissing, hmissing, hmissing, hmissing, hmissing, hmissing, hmissing);
Xls.Worksheet ws = (Xls.Worksheet)wb.ActiveSheet;
Xls.Range rng = ws.UsedRange;
Xls.Range hdr = rng.Find("Function Name", hmissing, hmissing, hmissing, hmissing, Microsoft.Office.Interop.Excel.XlSearchDirection.xlNext, hmissing, hmissing, hmissing);
string hdrAdd = hdr.get_Address(hmissing, hmissing, Microsoft.Office.Interop.Excel.XlReferenceStyle.xlA1, hmissing, hmissing);
string[] pcs = hdrAdd.Split('$');
string col = pcs[1];
int row;
int.TryParse(pcs[2], out row);
string methName;
row++;
while ((methName = App.get_Range(col + row.ToString(), hmissing).get_Value(hmissing) as String) != null)
{
App.Run(methName.Split('.')[1], hmissing, hmissing, hmissing, hmissing, hmissing, hmissing, hmissing,
hmissing, hmissing, hmissing, hmissing, hmissing, hmissing, hmissing, hmissing, hmissing, hmissing,
hmissing, hmissing, hmissing, hmissing, hmissing, hmissing, hmissing, hmissing, hmissing, hmissing,
hmissing, hmissing, hmissing);
row++;
}