Maybe I am different with this. Is she hiding something? Bad behavior? Not doing assignments?
My 9 year old (4th grade) knows how to scribble my initials same as I do. If it's one of those crazy nights nad I forget to sign it, she just takes care of it rather than get in trouble at school. I know, shame on me!! I honeslty don't think when my daughter does it it's a bad thing. She has my permission to do it if we forget. We have 3 kids that go in 3 different directions and some nights are just that hectic.
My sitter also has permission to sign it. She does the morning routine with the kids and comes at 615, when they are still sleeping. So either she or I will normally sign it. Minus my 7 year old. He has my husband and I take turns.
I signed things for my mom for school a lot too, we grew up the same. I'm one of 5 kids and my parents both worked and ran us in different directions after school...life gets hectic. If it was a bad thing we signed, we'd be in MAJOR trouble.
So I guess that's what I would do. Discuss with her WHY she is doing it. If it's because you guys are busy, I think maybe that's more on you. You should still be helping her to get it done. If it's because she is doing wrong, then that's totally not okay and I'd punish her at that point.
And before I get jumped on, there were maybe 1 or 2 kids who didn't do this when I was in school...so it's not like your kid is the 1st to do it or I'm the first mom to now freak out on my daughter for doing it.