Hi,
The pre-ancient stone carvings of Shiva depict him in his Pashupati Avataar. Pashu - Creatures/Animals + Pati - Lord. And as the God of the Animal Kingdom, he is shown bearing horns.
Since the beginning, he is depicted in many other forms (e.g. linga) and avataars as well, and still people worship Shiva in those same different forms or avataars and refer to him with over thousands of names.
It's just that the human God with moon crescent & snake necklace has, over the time, become a globally known (or widely commercialized) image of Shiva.
If I have missed out on any point or any of my information is wrong, I would love to be corrected.
Take Care