The best replacement for anyone is anybody.

The best alternatives to anyone are rated as following:
★★★★★  anybody
★★★★  everyone
★★★★  someone
★★★  anyone
★★  any one
★★  no one
★  anyone else
★  nobody
★  someone grammar
★  everybody
★  whoever
  anything
  have anyone
  do anyone
  someone difference
  has anyone
  whomever

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Speaking about anyone, one probably shouldn't forget about information.

Other search terms related to anyone and their ratings are:
★★★★★ information
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Google Trends

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anyone
anybody
everyone