MongoDb C# client: use existing property value as id or generate new

Question

I am migrating from RavenDB to MongoDB and therefore want to reuse existing classes deriving from

abstract class Entity
    {
        protected Entity()
        {

        }

        protected Entity(string id)
        {
            this.Id = id;
        }

        public string Id { get; private set; }

}

so far I register like this:

   BsonClassMap.RegisterClassMap<Entity>(
                x =>
                    {
                        x.MapIdField(b => b.Id);
                        x.SetIgnoreExtraElements(true);
                    }).AutoMap();

This works fine for inserting documents with already existing Id but fails for inserting documents that come without it. In this case I want MongoDb to create an Id for me. How would I do this without breaking anything else?

Edit: Maybe I need to point out what I mean by "fails". I mean that no Id is beeing generated by MongoDb. Id would always be null if not set by myself.