Select Multiple Fields from List in Linq

var selectedCategories =
    from value in
        (from data in listObject
        orderby data.category_name descending
        select new { ID = data.category_id, Name = data.category_name })
    group value by value.Name into g
    select g.First();

foreach (var category in selectedCategories) Console.WriteLine(category);

Edit: Made it more LINQ-ey!

Anonymous types allow you to select arbitrary fields into data structures that are strongly typed later on in your code:

var cats = listObject
    .Select(i => new { i.category_id, i.category_name })
    .Distinct()
    .OrderByDescending(i => i.category_name)
    .ToArray();

Since you (apparently) need to store it for later use, you could use the GroupBy operator:

Data[] cats = listObject
    .GroupBy(i => new { i.category_id, i.category_name })
    .OrderByDescending(g => g.Key.category_name)
    .Select(g => g.First())
    .ToArray();