In my organization, we are required to give feedback to our skip-level manager about my manager (skip-level manager is my manager's manager). In this questionnaire, which is generally a set of questions about different skills of the manager (interpersonal, technical, managerial, commitment, etc), we are required to rate our manager and write our feedback about him. The troublesome part for me in this is that there is an option to anonymize myself. So if I select it, I am anonymized to the skip-level manager and he won't know if I was the one who provided this feedback. Now, I have a very good relationship with my manager and he is pretty good in all measures in the questionnaire. I know the skip-level manager and we have a cordial relation (at least I assume so). Does it make sense to de-anonymize myself for this feedback?
Unless there's some highly sensitive information that you want to disclose, I would not suggest making this anonymous. In general cases like this one, anonymity does not help. In case the feedbacks are true and you expect some action to be taken based on that feedback, you should be able to own up the comments mentioned in the feedback.
Also note, a feedback does not always mean negative criticism (which usually does not go well with the recipient) - it also involves shout-out to the good things also and encouragement to carry on the good deeds. It'll be a good feeling for the recipient to get appreciated / acknowledged for the good they have done to people.
I would suggest against anonymous feedback in general. Assuming everyone is competent and wanting to improve, feedback will be generally used for improvements, and anonymous feedback means you can't be contacted to clarify or extend on what you said, making things harder for your skip-manager.
9 / 10 times, your writing style will uniquely identify you anyway. If your bosses know you well they can pick your writing style out from a pool even if anonymous anyway.
In general, (assuming your manager is a decent person and isn't extremely incompetent or some crazy nutcase) you should try to help your manager out in his performance reviews. A really good way to advance in an organisation is to help your boss get promoted.