Often, we think of our identity as something fixed and singular. We certainly talk about groups who share some common characteristic as though they were clones; we speak about 'the black experience' or 'the female experience' or whichever group we're discussing as through the were dots on a statistical model. But as much as I enjoy a good scatterplot, we are all unique experiential snowflakes who have many component parts to our self-identity. Furthermore, what we consider the most prominent or important piece of that multilayered description varies with our environment and continuing experiences.
When writing a character, it's easy to fall back into the habit of constructing identity as singular. The character has a single key feature-- culture, attractiveness, age, intelligence, or a cool superpower, and that's the fulcrum around which their personality and plot arc revolve (all other characteristics are presumed 'normal', which is a can of worms for another day). This is fine for walk-on characters, but for a major character it's worth investing time exploring the facets of their identity and how that character expresses themselves in different situations.
It is important to consider as well that a character's self-identity may differ from assumptions that other characters make, or features that other characters see as important (which gives you a chance to show some of the underlying power dynamics in your setting). Characters may hide parts of their identity, or be totally oblivious to parts of their identity that they see as a 'default', or perhaps they simply have different priorities than the other characters. Just working out some key points about how your character self-identifies and how they present themselves in different situations puts you a good portion of the way to developing a realistic and interesting character.