Yes, I think when people retire, their identities continue to develop. No, they do not lose their professional identity. How could they? They did work for decades, right? And although they may not punch the timeclock anymore, the way they work with people, they way they approach projects or tasks in their personal lives has been shaped by what they did in the professional world. Furthermore, people who worked from home, at home, or for only two years also have this professional aspect to their personality as well.
The only reason I include this is that the current party line is that "I am not my job"; and I say bullshit to that. You really are partly defined by the work you do. To think your identity is not largely affected by this is just too woo-woo for me to buy into.