V.E.R.A. -- Virtual Entity of Relevant Acronyms (February 2016):

GREP
       Global Regular Expression Print (Unix)


The Jargon File (version 4.4.7, 29 Dec 2003):

grep
 /grep/, vi.

    [from the qed/ed editor idiom g/re/p, where re stands for a regular
    expression, to Globally search for the Regular Expression and Print the
    lines containing matches to it, via Unix grep(1)] To rapidly scan a file
    or set of files looking for a particular string or pattern (when browsing
    through a large set of files, one may speak of grepping around). By
    extension, to look for something by pattern. ?Grep the bulletin board for
    the system backup schedule, would you?? See also vgrep.

    [It has been alleged that the source is from the title of a paper ?A
    General Regular Expression Parser?, but dmr confirms the g/re/p etymology
    --ESR]


The Free On-line Dictionary of Computing (30 December 2018):

grep

     A Unix command for
   searching files for lines matching a given regular
   expression (RE).  Named after the qed/ed editor
   subcommand "g/re/p", where re stands for a regular expression,
   to Globally search for the Regular Expression and Print the
   lines containing matches to it.  There are two other variants,
   fgrep which searches only for fixed strings and egrep which
   accepts extended REs but is usually the fastest of the three.

   Used by extension to mean "to look for something by pattern".
   When browsing through a large set of files, one may speak of
   "grepping around".  "Grep the bulletin board for the system
   backup schedule, would you?"  See also vgrep.

   [Jargon File]