Pam, your anxiety comes through loud and clear, and I'm excited that this forum is here to turn to for clarity and comfort.
As I understand your situation, you have finished at least some sections of a memoir and let some friends read what you've written. Your story divulges some pecadillos of theirs? So they have asked you to change the name?
Hey, if that's all they ask, that you let them wear a mask, so to speak, what's the problem? This story is about you, and you have every right to expose anything about yourself that you wish. But why would you knowingly invade your friends' or relatives' privacy and cause them grief? It doesn't sound like they asked you to remove the section that involve them. I'd consider that quite a compliment. Why not let them choose their new name?
Consider whether it will diminish the story in any way or compromise your Truth to change this/these names? If the answer is yes, the next question is whether it's worth causing grief and damaging your relationship with these people? And possibly risking legal complications...
I'm guessing that your story will perk along quite nicely with new names!
