Hi Mirjam. *s* The article I referred to in my post is one I posted earlier (post title Hoor and Narmer).

Yes, the falcon is represented on the serekh to represent kingship - however, whether or not that falcon deity was specifically Horus has yet to be ascertained (one mustn't forget the falcon god of Nekhen - aka Nekheny, nor the fact that Nekhen played a very important role in the lives of Pre and Early Dynastic chieftains). And as with most things during this period, there is a certain amount of the unknown which must be factored in.

One must admit that Pre and Early Dynastic hieroglyphs, when written, are a bit messy, so to speak. Not to mention being difficult to decipher. There is also the chance that some of the very earliest kings' names were the names of animals (ie possible names of Crocodile & Scorpion which are speculative).