Hi Fredrik!

If I were you I would add new field to the index which contains the names of the media items. Right now the multiple media picker is saved as JSON in the index. So that's why they aren't showing up! I would do something like this:

public class IndexComposer : IUserComposer
{
    public void Compose(Composition composition)
    {
        composition.Components().Append<IndexerComponent>();
    }
}
public class IndexerComponent : IComponent
{
    private readonly IContentService _contentService;
    private readonly IExamineManager _examineManager;

    public IndexerComponent(IContentService contentService, IExamineManager examineManager)
    {
        _contentService = contentService;
        _examineManager = examineManager;
    }

    public void Initialize()
    {
        if (!_examineManager.TryGetIndex(UmbracoIndexes.ExternalIndexName, out IIndex index))
              return;

            ((BaseIndexProvider)index).TransformingIndexValues += IndexerComponent_TransformingIndexValues;         
    }   

    public void Terminate() { }

    private void IndexerComponent_TransformingIndexValues(object sender, IndexingItemEventArgs e)
    {
        if (int.TryParse(e.ValueSet.Id, out var nodeId))
        {
            foreach (var fieldValues in e.ValueSet.Values.ToList())
            {
                if (fieldValues.Key == "relatedDoucments")
                {
                    var node = _contentService.GetById(nodeId);
                    var documents = node.GetValue<IEnumerable<IPublishedContent>>("relatedDoucments").Select(x => x.Name);
                    e.ValueSet.TryAdd("searchableDocumentNames", string.Join(" ", documents));

                }
            }
        }
    }
}

I wrote this a bit hasty! It should probably have some more if checks. But let me know if it works!

//Johannes