Cool! I ended up deciding that the node name hadn´t got to be descriptive since instead I just show the datetime property in the list view ("Tidsrum" is Danish for "Time span").

So I ended up with this code:

using System;
using System.Linq;
using Umbraco.Core;
using Umbraco.Core.Composing;
using Umbraco.Web.Editors;
using Umbraco.Web.Models.ContentEditing;

namespace My.Website
{
    [RuntimeLevel(MinLevel = RuntimeLevel.Run)]
    public class SubscribeToEditorModelEventsComposer : ComponentComposer<SubscribeToEditorModelEvents>
    {
    //this automatically adds the component to the Components collection of the Umbraco composition
    }

    public class SubscribeToEditorModelEvents : IComponent
    {
        // initialize: runs once when Umbraco starts
        public void Initialize()
        {
            EditorModelEventManager.SendingContentModel += EditorModelEventManager_SendingContentModel;
        }

        // terminate: runs once when Umbraco stops
        public void Terminate()
        {
            //unsubscribe during shutdown
            EditorModelEventManager.SendingContentModel -= EditorModelEventManager_SendingContentModel;
        }

        private void EditorModelEventManager_SendingContentModel(System.Web.Http.Filters.HttpActionExecutedContext sender, EditorModelEventArgs<Umbraco.Web.Models.ContentEditing.ContentItemDisplay> e)
        {

            foreach (var variant in e.Model.Variants)
            {
                if (variant.State == ContentSavedState.NotCreated)
                {


                    if (e.Model.ContentTypeAlias == "SiteEventTimespan") {
                        variant.Name = "Time span";
                    }
                }

            }

        }
    }
}