Is it professional for people to ask where you are going next when you leave?
A coworker announced that she'd be leaving. Others ask about the next gig. I feel there's no need to ask or answer this question.
Everyone asks. Some people ask that anyone curious speak with them privately to learn where they're going, but I and nearly everyone else just say it outright.
I don't think its unprofessional. It's just that the person may not be willing to answer in front of everyone. So maybe better to ask privately.
You can ask, she might not disclose now but may be later when she joins the new company
If you don’t tell your management, how would they find out if you are going to a competitor?
People are curious as to where you’re going, but in reality nobody cares that much. People ask just out of natural curiosity. Very rarely is it any deeper than that.
It seems like a pretty normal question to me. Would only be an issue if you're going to a competitor. Good way for people to stay in touch which can be helpful for your career.