Sorry if this is a foolish question, but is this something that requires cryptography to solve? If Alice wants Bob to know that a payment came from her, why not simply add a text from field to the onion that gets encrypted to the recipient that can say: from: Alice?
That would allow someone else to pay Bob while claiming to be Alice, but is that a risk? (That’s an honest question.) It seems like it might actually be a feature: I occasionally make payments on behalf of other people, e.g. when I order a pizza but my partner will be picking it up; it’d be nice if I could simply set the from field to the name of the intended payer.