No. They don't. Not when you are fully transitioned. Early on, yes.
I have run into a lot of people who knew me before, who have no idea I am the same person. If I don't care about them, I just introduce myself as Jay, as if I have never met them, and life goes on. If I care, I might tell them (hasn't happened yet). One was a former client who hated me. After I saw her, she loved me! I thought that was hysterical she had absolutely no idea I was the same person.
Jay