The Taoist cosmology is my favorite place to look for such fantastic structures. The constant flux between yin and yang is very convenient to apply to wave-mechanics driven creatures, and if you want a "energy being," which has no matter, you are almost certainly going to be dependent on standing waves to give them a presence.
In the Taoist cosmology, the world starts in wu ji, literally translated as "without ridgepole." This is unlike our "empty space" in that it has chaotic flow within it, but no particular definition. Or perhaps this is exactly like our "empty space," if you use Quantum Mechanics to look at the fleeting virtual particle pairs that jump in and out.
At some point, a single point crystallizes into an entity with an identity (such as one of your energy beings). At this point, the are treated as a taiji, literally "great ridgepole," which means they have a yin and a yang side. This taiji grows outward until it reaches its limits.
Yin and yang are brutally hard to define in Western terms, but with respect to energy flow and waves, it is reasonable to define them in terms of directions of flow. Yang is flow outwards, and yin is flow inwards. I mentioned standing waves earlier. It is trivial to see a standing wave between two points which are oscillating back and forth between yin and yang, pouring energy from one to the other.
These in and outward flows are key because your creature lacks any physical form to keep its structure. It needs some structure to give it an "identity," otherwise it's simply nothing. Defining that structure in terms of yin and yang saves you a great deal of work reinventing things. Using yin and yang to create this structure is very powerful because the Chinese spent thousands of years working with those terms, so there is a massive body of material for you to draw from; you don't have to invent the entire energy-being system yourself!
For instance, it points to how the energy beings could interact with physical beings. If you tried to drive a taser into one, it could softly allow you to push its structure away, but never actually breaking its structure. Meanwhile, it could search for very low energy solutions to its problem, such as reaching its energy into your brain, and softly nudging the electrical energy in the motivation part of your brain to end your resolve to use the taser (it might even channel a tiny bit of the taser energy to do so... waste not, want not).
On the other side, if truly threatened (perhaps it could not softly move away from the taser), it can do what is known as fajin, having all of its body shift to yang, generating a massive outward expansion of energy to blow you back. (obviously this comes at a great energy cost)
It also shows how larger groupings could form, like energy-bactera biofilms. All they need to do is balance yin and yang, and develop a structure which is hard to rip apart.
In fact, one could even argue for larger energy beings. The Chinese philosophy has a long tradition of the concept of "animal spirits," such as the spirit of the tiger, or spirit of the bear. When kung-fu schools develop forms such as "tiger kung fu," they attempt to capture that animal spirit, to the best of their ability. If you needed larger energy beings with personalities, developing them after these animal spirits would be a very effective way of capturing something useful for your story, without having to work out all of the fine details of how energy can communicate and interact.