When you call GetContentResult(), you are actually loading the matching content from database (or cache, if cached). if you want specific field (not limited to your CategoryName), you would have to use GetResult() as a projection of the document 

Thanks for the answer, Quan.

Hm when I call the GetResult for the ProductContent, I get the exception:

EPiServer.Core.EPiServerException: Please use GetContentResult extension method for getting results with content types

How can I get the product content with GetResult?

How does your code look like? Did you just change the last line to GetResult? you would also need to remove the Search<ProductContent>(). instead: Projections (optimizely.com)

it might not be trivial change 

For now, the full search is as following:

var result = SearchClient.Instance
                         .Search<ProductContent>()
                         .Filter(x => x.CategoryRouteSegment().MatchCaseInsensitive(categoryRouteSegment.ToString()))
                         .FilterOnCurrentMarket()
                         .FilterOnLanguages(new[] { currentLanguageCode })
                         .FilterForVisitor()
                         .OrderBy(x => x.SortOrder())
                         .Skip(paging.Skip())
                         .Take(paging.PageSize)
                         .GetContentResult();

So, if I would remove Search<ProductContent>() then - should I match type property with Product Content manualy and have something like ForQuery("*")?

You need to be using something like this

var result = client.Search<BlogPost>() .Select(x => new SearchResult { Title = x.Title, Author = x.Author.Name }) .GetResult();

i.e. a Select query for projection. it might not provide all you need, so you might be forced to load the content yourself (tip: using GetItems is a good way to ensure performance) 

Would that be possible for the Product content? Because I got the exception when using GetResult on that:

EPiServer.Core.EPiServerException: Please use GetContentResult extension method for getting results with content types

Yes it should. But the Select part is important because you are getting a projection. Your query should look like this (untested by me obviously)

var result = SearchClient.Instance
                         .Search<ProductContent>()
                         .Filter(x => x.CategoryRouteSegment().MatchCaseInsensitive(categoryRouteSegment.ToString()))
                         .FilterOnCurrentMarket()
                         .FilterOnLanguages(new[] { currentLanguageCode })
                         .FilterForVisitor()
                         .OrderBy(x => x.SortOrder())
                         .Skip(paging.Skip())
                         .Take(paging.PageSize)
                         .Select(x=> new SearchResult {Name = x.Name, ContentLink = x.ContentLink})
                         .GetResult();