Yes, they can. I have met only one God like this personally. There is a lot of information that the Gods have and that is not publicly available, about them and about the world, because a lot of people are not ready for it. As the quote from Maxine I remember since dedication "The more you know the more you can know", the more knowledge you have the more ready you are for more advanced knowledge.
i read on the forum years ago that even the sigils and names of the gods were very different, but they did not use them to avoid enemy attacks. But forums are a public place. i couldnt verify its truth