There is not currently any way to do this, so it would be a feature request. There is a lot of discussion on meta about anonymising users upon request, but I don’t think there has been anything about automating it.
Some reasons I can think of:
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Reading old discussions without the context of names/avatars can be very confusing
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The user may return, and want to re-claim their account. This could be especially true on support communities, where users only visit when they have a problem.