I've heard others with that same fear, and sadly it stopped them from taking advantage of a medicine that could significantly improve their quality of life.

Depression and anxiety, even when mild, can be pernicious in their self-preservation. Self-identifying with a symptom, and avoiding a potential cure because "it could turn you into an entirely different person" by removing that symptom, is often the disease talking.

SSRIs don't turn you into a different person. When working properly (i.e., right dose, right med), they simply give you more mental space to deal with and work through problems. Who you become after working through your issues is entirely up to you.