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In the new profile management world, you can find yourself using a super old
profile named by default "Default Profile". These names should be migrated to
the new style default names ("Person 1").

The code is fantastically special because the ProfileInfoCache re-sorts itself after
each rename, so doing a batch rename is really not a thing it wants to do.

BUG=406409

Review URL: https://codereview.chromium.org/490363002

Cr-Commit-Position: refs/heads/master@{#291598}