Naruto could act impulsively and make hasty decisions that seem unthoughtful. This would make others think he's not very intelligent. He might also avoid getting into deep conversations where his true intelligence could be revealed. By constantly changing the subject or making jokes, he can keep people from realizing how smart he is.
He might use simple language on purpose. For example, he could pretend to be confused about things he actually understands well. He may also make silly mistakes intentionally to give the impression that he's not as smart as he really is.
One way Naruto could hide his intelligence is by relying on his more boisterous and energetic personality. He could play up the part of the simple - minded, fun - loving ninja. He'd be the first to volunteer for physical tasks rather than intellectual ones, and when it comes to strategy discussions, he might act like he's not really following along, when in fact he has his own brilliant ideas but just doesn't want to show them yet.
He might want to protect himself. If others know how smart he is, he could become a target. Enemies might see him as a greater threat and go after him more aggressively.
He might put on a fake smile and act normal. Naruto is good at being energetic on the outside, so his family may not suspect that he's in pain.
In many fanfictions, Naruto might hide his pain by putting on a big smile. He's always been the type to try and be positive in the face of his friends. He could also distract others with his goofy antics, like making a joke or doing something silly to shift the focus away from his inner turmoil.
He might pretend to not understand complex concepts. For example, when others are discussing advanced magic theories, he could act confused even though he actually gets it.
He may also choose to stay quiet during discussions where his knowledge could shine through. Instead of speaking up and showing off his intelligence, he lets others do the talking and only chimes in when it's necessary or when he can play dumb and ask simple questions.
He could be using basic chakra control techniques to suppress his power. By constantly regulating the flow of his chakra, he can keep his true power hidden. For example, he might be using a form of internal chakra suppression similar to what some ninja use to hide their presence.
He might use some special jutsu or seals. For example, he could use a sealing technique to suppress the signs of his bloodline. This way, others wouldn't be able to detect it through normal means like sensing chakra.
Well, in fanfictions, often the plot takes a different turn. Naruto might hide from his family because there could be some sort of misunderstanding. For example, there could be false rumors about him being involved in something bad. And he might think that his family would believe those rumors without giving him a chance to explain. So, to avoid the immediate confrontation and judgment, he chooses to hide.
Well, he might use simple distractions. For example, he could create a minor commotion to draw attention away when he's about to use a particular skill subtly. Maybe he pretends to be clumsy or make a small mistake on purpose so that others don't suspect he has advanced skills.
Maybe he is afraid of being bullied. Smart kids sometimes get picked on by others who are jealous.