You can, to a point. In so much as we've abstracted it to be a bit of paper. But can you really take a Frenchman and make him something else, or will he always, in a sense, be a Frenchman?
I can answer that, as I have changed nationality. See, I grew up in a tiny far away country nobody ever heard of, which I'll call Xland. As a young woman I married a German man and moved to Germany and after a few years got German nationality, which is of far more external value than Xland nationality. Sorry, Xland, I had to abandon you. Germany does not allow dual citizenship.
Now, the stereotype of an Xlander is just about the opposte of a German. Xlanders are, typically, friendly, happy go lucky, unpunctual, casual, not much bothered about doing things properly (you might. for instance, find a bathroom hook screwed on upside down). Not to diss Xlanders; they just don't take it all too seriously, which is probably why Xland remains one of the poorest and most backward countries on the planet.
Germans (the stereotype) are the opposite. They are obsessively punctual, meticulous, attentive to rules (ever seen a German waiting at a red pedestrian sign when there's no car in sight?) and to minute details, perfectionist in all they do, and, yes, a bit unfriendly and formal.
I had a hard time adjusting, but adjust I did. I thought some of these qualities were actually good for me as I tended to have a slapdash attitude to life, so German traits balanced me out. After more that 40 years in Germany I was an exemplary German. I knew exactly how to behave, to clean, to take care of details, to be attentive and not to dream around so much. I had a responsible job and a good pension. Hurrah! I'd made it!
That's when I'm in Germany. When I go back to Xland, I can be as dreamily casual and slapdash as I like, though I notice a small annoying tendency to view everything through German eyes, to be critical and even a bit supercilious -- uh-oh...
In the end I see both "identities" as just a collection of traits, characteristics, attributes. I can don one identity and discard it at will. I am not attached to either -- I adapt as necessary.
And yet, and yet the attributes I was socialised in, my Xland background, is the one I love more, feel closest to. The German one is like a disguise, a role I'm playing, even though those qualities are now second nature to me. And I don't feel it in any way impinges on my original Xland "identity". I'm not diminished by being German. I feel completely accepted and integrated in Germany. I don't have to have anyone validating me as either an Xlander or a German I adapt as I see fit.
I guess it all explains why I also can't take gender identity seriously. I believe that clinging obsessively to any identity, whether of gender or nationality, is harmful. It binds you down. It's all not real, just a bundle feelings and traits and characteristics, and they limit us to a very narrow path in life. It's good to let go and just BE, not be something-or-other, woman or man or German or Brit or Xlander
Germans who cling to their stereotypical traits have a horrendous time when they travel abroad to countries where it's not all planned out and meticulously clean. They are not free; they come across as pedantic old farts constantly complaining. Germans who are flexible have a good time; they can let go of their German skin and adapt. I know both types.
(But I have found a wonderful compromise through moving to Ireland. Xland friends of mine who came to visit said that Ireland is the Xland of Europe, and it's true!)
And to answer the question at the top of this post: Yes, I will always be an Xlander at heart, since Xland formed my personality. But I have some say in the matter and I am not bound by any typical Xland traits.