You didn't tell us, if your data is nested or just flat.

Perl doesn't allow to change keys in place, you either need to copy to new a hash, or delete and recreate every single key to be transformed. If the hashes are nested you need to walk thru the tree.

If I were you I would just check if the JSON string has a pretty format which allows a simple regex to translate keys only.

update

proof of concept:

  DB<100> use JSON

  DB<101> $hoH = {
             nested => { crossReference => 42, incidentAbstract => "st
+ring" },
           }

  DB<102> $str = (new JSON)->pretty(1)->encode($hoH)
{
   "nested" : {
      "incidentAbstract" : "string",
      "crossReference" : "42"
   }
}

  DB<103> %translate= ( 
                      'crossReference' => 'cross_reference' ,
                      "incidentAbstract" => 'abstract',
                      )

  DB<104> $or_keys = join "|", keys %translate
 => "incidentAbstract|crossReference"

  DB<105> $str =~ s/^(\s+")($or_keys)("\s+:)/$1$translate{$2}$3/gm
 => 2

  DB<106> $str
{
   "nested" : {
      "abstract" : "string",
      "cross_reference" : "42"
   }
}
[download]

of course this can also be done with Data::Dumper ...