Of course it is. Even when raised in similar circumstances, people relate and respond to events differently. Not everyone is the same, not everyone has the same level of natural talent, not everyone will develop the same set of social skills, and some children will be more likely to develop natural leadership skills.
Some kids will buy into and believe in what they are being taught, others may become more skeptical over time. Some will rebel, though the strength of their rebellions will depend on the limits they are placed under, and others will toe the line. You’ll get the ones who are intelligent enough to ask questions and the ones who are so intelligent that they know asking questions is a bad idea.
There’s a myriad of possible personalities and the way to discover them is to sit down and work with your characters. Think about how each would respond to a specific situation, how does what X might say differ than Y? The differences may be subtle, but even slightly different phrasing or tone can indicate a different response. Think about the adults and minor characters, what do they think about your individual characters? Someone’s probably fallen behind in their training, maybe someone got caught daydreaming. Who do they like? Who causes trouble? Do different adults have different opinions on who their favorites are? Do the troublemakers cause violent or non-violent trouble? Do they aim for high risk targets like the teachers and older, more dangerous students or ones who can’t fight back like the serving staff and younger kids?
One may be talented and hard working, everyone probably hates them because they make them look bad. One will probably be talented but lazy, they may have at least a few toadies. There’s going to be at least one who is on the outside looking in.
These are just a few suggestions. Just sit down with your setting, with the characters in them, and start thinking through what happens there. Not in the context of the greater plot, but in small moments, the day to day minutia. What do they do? What hobbies do they have? Who looks after them and takes care of them? Are they raised in a barracks, did they ever have or will ever have some sort of fostering system? Mentor program when they finally come of age and have to choose a profession? Who took care of them when they were babies?
Soldiers in the military have different specializations and roles, maybe one of your kids is being groomed for command while their friend is about to get shuffled off to logistics. Even within a very specific range, these kids will eventually have to develop specialties. Things will change for them and how they respond to those changes and challenges both during their training and when they encounter what they’ve been trained to do will be what defines them.
Always give your characters a chance to tell or show you who they are. Once you’ve settled the sameness of their circumstances, then you can define their differences.