Hi. The first thing is that it depends on what story I am writing. But, assuming the characters are human, I also wonder if they belong to Earth or not. In the case that they are earthlings (argh, the Ak Ak Ak Ak escaped me! I will prefer to say terrestrials), I base myself on what already exists and make an extrapolation to a hundred or a thousand years or whatever I need and from there just I do a questionnaire.
This questionnaire can be as extensive as you want or only refer to a few aspects. But the fact that it is an inherited pantheon of terrestrial culture, however precarious the prospective aspect of the outline may be, one wants it or not anyway something will survive through time. Certain customs, superstitions or dogmas will be preserved or at least will change depending on the time.
For example, in ancient times the European gods were lunar while the American gods were solar. So, especially if the characters in your story come from Earth, I repeat, a hundred or a thousand years have passed, you should still consider at least a certain evolution.
On the other hand, if your story occurs in a fictional world, well, there you already have complete freedom to create other types of gods.
Still, even in a very basic way, I would advise you to think of a certain cosmogony. For example, we have a notion of how the Universe was created. Now what is your characters' vision about their own particular universe? The planet where they live, is it a relatively new world, in the middle of terraforming or already in frank decay? In short, the birth of religions is linked to Astrology. That creates a set of beliefs and superstitions, a way of seeing things. For example, in 1800 the Arab peoples lived terrified to a eclipse and every time there was one they used to predict a thousand misfortunes. And it was just a simple eclipse. BTW, is there a moon on your planets? Maybe there are two suns, like in Star Wars. Maybe they are in an asteroid belt. So, as you will see, depending on how your worlds are, the variables change.
However, perhaps you could take advantage of what you said about certain ancient beings whose rise has placed them in a superior position compared to other inferior races. Maybe the point is that these beings are not as, as gods or as powerful as they claim and that is why they go with secrets and all that. Maybe they are even deadly. BTW, how long do people live in your world? On what do the gods of your story base their power? In this regard, This immortal, by Roger Zelazny, is a sci-fi novel that could give you good ideas for your story.
Because giving them a name is the least of it. That's the easiest thing to do, actually. I personally do not have a method for baptizing my creatures. I just have a query summary with five pages full of names that I have invented to baptize anything; not just a character.
I hope I've been helpful.