The title lays out my thesis in perhaps the maximally provocative way: if you put direct effort into keeping your identity small (à la Graham), you are doing harm to yourself akin to the kind of harm you do to yourself by suppressing emotions.
I was inspired to write this after reading some of the recent discussion on the EA Forum about why people do or do not identity as an EA. Responses that mention not wanting to identity as EA in the name of keeping one's identity small got me thinking about this topic and made me realize that, despite likely being somewhat less attached to various identities than average, I don't eschew being identified with things or using identities as a means of communicating with others. And I immediately had a strong sense of why I don't do that: taking action to directly avoid having a large identity would be trying to control myself in a way that leads to cognitive dissonance and dissociation at best and cognitive fusion at worst.
Here's what I see going on. A person realizes they are identifying as or with something, let's say effective altruism since that was the motivating example. They have a commitment to keeping their identity small, so give themselves feedback that they are doing something wrong when they identity as an effective altruist and should stop doing it. Negative reinforcement like this, though, rarely makes the underlying reason for wanting to do something go away, like perhaps wanting to signal that you are the kind of person who cares about everyone equally and thinks rationally about things. Instead it creates a secondary desire to not do the thing that lives alongside the desire to do it. So now you both want to identity as an EA and don't want to, and whether or not you do it depends on which desire is stronger.
A good model of what happens next is offered by Internal Family Systems: competing parts of the brain are now engaged in a battle of trying to protect you from what other parts of your brain want you to do. Aside from causing a lot of suffering as a result of being the battleground on which this fight occurs, it can eventually lead to isolation (exile) of those parts of the self that seek to identify with something. They're still there trying to do their thing, of course, but they are so well suppressed that they become hidden from self-awareness.
I see this as analogous to the effects of suppressing emotions in order to control them. Maybe you can do it, but rather than true mastery of emotions it causes suppression of the ability to see what is happening. The result is often that rather than getting, say, scared, you instead think the world is out to get you as a result of cognitive fusion that happened as a result of suppression. The path back out is through things like focusing and studying the self to forget the self.
None of this is to say I disagree with keeping your identity small as a useful direction, but it's more the kind of thing to check in on occasionally to see if it's a consequence of other things you're doing rather than something you can go directly towards, since the direct path, as argued above, makes things globally worse even as you seemingly make local improvements. Small identity is something that best happens as a consequence of other habits of mental health and self-awareness, not as a direct target. Compare notions like effortlessness, trying not to try, not trying to try, and global wayfinding.
Put another way, don't Goodhart yourself on keeping your identity small. Instead focus on nonmonotonic Pareto improvements that, as a consequence, will eventually make everything better, including less identifying with things.