if it's a choice it will soon become a non-choice since if some people on a small team decide not to be anonymous it will be obvious who is whom anyways.

If anonymity is optional there will also likely be some implicit pressure coming from management not to be anonymous, leading to people censoring their true feelings for fear of repercussions ("so, I've noticed for the past few weeks you haven't been happy or productive, maybe this is not a good fit for us")

Not sure, maybe I am being too negative, but when it comes to anonymity and workplace surveys my default setting is "the more the better"