What is the name for the copies of a paper that you receive once it's been published?
They are called offprints.  From Wikipedia:


  An offprint is a separate printing of a work that originally appeared as part of a larger publication, usually one of composite authorship such as an academic journal, magazine, or edited book.
  [...]
  
  Offprints are used by authors to promote their work and ensure a wider dissemination and longer life than might have been achieved through the original publication alone. They may be valued by collectors as akin to the first separate edition of a work and, as they are often given away, may bear an inscription from the author. Historically, the exchange of offprints has been a method of correspondence between scholars.