The very first story I ever wrote was written from the perspective of a collective mind. So, as they say on /b/, this question is very relevant to my interests.
I would approach the concept of an intergalactic hive mind from the perspective of sociology, neuropsychology, and biology. A hive of bees can be considered as a single organism: only the queen can reproduce, the drones have the status of ejaculate (of which only one sperm will fertilize the egg and the rest die) and the workers are the limbs of the hive that have no individual goal, only strive to provide for the hive. At the same time an individual bee does in fact provide for itself (it would be useless for the hive, if it didn't eat or rest and died), and clearly shows individual behavior independent of the hive.
The human brain, too, while apparently a unified organ creating a single consciousness, contains a not insignificant number of correlated but independent processes. For example, you can walk and talk at the same time. In fact, you can walk without having to consciously take care of that, so "something" inside you is regulating that behavior while your mind is otherwise occupied. Therebare people who have lost half their brain and still live and function quite normally -- so what was that part of the brain for? There are distinct parts in your brain that have different functions much like the individual bees in a hive: one part takes care of your inner organs, another processes visual information, one regulates emotions, and so on. This is a simplified view, of course, and in truth many functions are spread out over many parts of the brain (just like many worker bees collect food, and many take care of the eggs), but no function involves the whole brain.
You can find analogies in sociology and other sciences yourself, and I'm sure you're already able to see what I'm getting at:
A hive mind, while interconnected, does not necessitate that all parts are directly connected to all others (that would be dysfunctional), that all parts are always "on", that all parts are the same and have the same functions, or that individual parts have no other functions besides thoae related ro the hive. On the contrary, it would be highly functional if individual hive members could think and take care of themselves if they ever got disconnected from the hive (e.g. due to transmission failure or disease). In fact, if all of the hive but one member died, it would be good if that member had the potential to "turn into a queen" and start a new hive.
It is very unlikely that a hive mind would have unified thinking. If it had, all members all axross the universe would have to eat and sleep at the same time and walk in lockstep. Obviously that won't work. Individual members will encounter individual problems that tjey have to take care of, and a myriad of these problems will happen at the same time. Therfore it is highly likely that individuality will remain in existence in the individual members of a hive mind, to a not inconsiderate degree. They will have individual consciousness, individual emotions, and individual goals that will interact with the hive's goal not unlike the differing and often contradictory and mutually exclusive aspirations that humans today often experience.
Some people believe that meditation and other spiritual practices connect you to the universe and all living beings inside of it. Yet spiritual masters aren't mindless ants, remote controlled by the universe. They are very much individuals, despite feeling themselves in tune with what the univerae "wants".
From all this follows that you can write a story about a hive mind both from the perspective of an individual member (in first or third person singular), from the perspective of a temporary or pwrmanent functional subcollextice (in first or third person plural), or -- though that will be difficult to conceive of, because it lies so far outside or experience -- drom the perspective of the total mind itself. I imagine that latter perspective to be a xacophony of a myriad synchronous thoughts -- and unreadable.