Is it manipulative to adapt to my boss's personality?

No, it's professional. You adapt to clients, colleagues, and friends constantly. Adapting to your boss is the same—it's communication, not fakeness. You're changing your delivery (style), not your values (content). Good employees speak the language their boss understands.

How do I know what personality style my boss has?

Observe: What energizes them? (People = Influence; Results = Dominance; Process = Conscientiousness; Harmony = Steadiness). How do they make decisions? (Fast = Dominance, group consensus = Influence, data-driven = Conscientiousness, collaborative = Steadiness). Notice their communication preference: email (detailed), quick chats (fast), long meetings (relationship-focused).

What if my boss's style is the opposite of mine?

You're not incompatible; you need to learn to communicate. An introvert-boss to extrovert-employee: the employee learns to work independently and give written updates. An extrovert-boss to introvert-employee: the employee learns to share more verbally and in meetings. Small adjustments prevent big friction.