OK-- well, this is advice from a parent whose child STILL does this for social reasons, and she's in college.
There are two varieties of social hiding of high ability, in my own experience:
1. hiding one's actual age, or "padding" it to make those who are older feel less uncomfortable with you. This goes through a low spot in early adolescence, but generally +/- 1-3y is within the realm of believable. DD doesn't LIE about her age-- but she lets others believe whatever they want, if that makes sense. This is the strategy employed by her as someone who has been accelerated 3-4y.
2. What your child is doing-- which is also sometimes termed "dumbing down" but is really about not wanting others to dislike them, not wanting to be the center of attention, not wanting to be socially isolated, and-- legitimately, (IMO) not wanting other people to feel BAD just because the person with such high ability actually exists.
Honestly, I'd acknowledge that the problem is real. THEN, and probably only then-- can you discuss what might be some "better" solutions to this problem.
This is a lifelong problem, and I think that you're right to be concerned about it.
One thing that DH and I (we're also HG+) have learned over the years is that only sharing PARTS of ourselves with others tends to be the way to go. That is, in a setting which is about, say... tying flies (totally made up)-- it's okay to be really really good at that thing, highly competent and almost obsessed-seeming. About that one thing. But don't chit-chat about much else with those people, in general... because when they learn that you're a polymath that is "that good" at everything ELSE, too-- that is when you turn into a space alien.
In some ways, while there is a limit to being pointy and acceptable, being well-rounded and at high LOG is less acceptable up to that point. Polymaths feel threatening to other people. Please don't try to deny this reality for kids-- the ones that are socially perceptive already know that it's true.
Examine the reality, and discuss costs and benefits for different solutions to that problem. For some kids, having a peer group that accepts them and embraces them is more important. As individuals, we all have to find out how much of our "real" selves we can be and live with the social consequences. We can't change the world. Only what we as individuals do in it.
This is an adult-sized problem that is foist upon HG+ children at very young ages. That is deeply unfortunate-- but it's the same basic problem that all adolescents have to wrestle with, developmentally, as they grow to become adults.
I don't know if that helps any-- but I'd caution parents NOT to deny a child's lived experiences and their autonomy about this choice. Just call it out, and discuss the consequences. Not all kids want to operate on par with their potential.
