The Value property of DefinedName (implementing ISpreadsheetName) always returns a result with a General format, which is very impractical when the value is for example a date. There should be an option to get a formatted result as well.
A possible workaround for this missing functionality would be to parse the RefersTo value and find where it points in order to grab the format:
Workbook workbook = new Workbook();
Worksheet ws = workbook.Worksheets.Add();
ws.Cells[0, 1].SetValue("2/1/2013");
ws.Names.Add("MyField", "=Sheet1!$B$1", new CellIndex(0, 0), "My Field");
string value = ws.Names["MyField"].Value;
CellRange range;
bool success = NameConverter.TryConvertCellRangeNameToCellRange(ws.Names["MyField"].RefersTo, out range);
CellValueFormat format = ws.Cells[range].GetFormat().Value;
string result = ws.Cells[range].GetValue().Value.GetResultValueAsString(format);