Why are authors not made anonymous during the review process?
Sometimes they are. That's called double blind refereeing. It is becoming more common.

From https://www.maa.org/press/periodicals/guide-for-referees


  The Board of Governors of the Mathematical Association of America has
  mandated that our journals use a double‐blind review system.


This blog post and comments discuss the history, pros and cons of double blind refereeing in  parts of mathematics and computer science.