it's easy to say "you should sue" but that's a lot more difficult in practice.
This is the second time in a few months that I have seen this issue crop up:
I fear that this situation will not last. I just googled the name, and curiously, the knowledge panel has a little link that says "claim this knowledge panel." Do you see that option; have you tried exercising it?
Yes you could sue for that but I doubt that is what the pastor should sue for, as you said she was threatened after being mis-identfied as you, they were told of their error, they recognized it and removed her picture, then they put another one in of her again.
I think the pastor should talk to a lawyer from her state as to what she can sue for.