If you regular expressions as your keys, then you save the overhead of recompiling them everytime. The qr// operator does this for you.

my %Ren2Dol = (
    qr(rrv193\d{4}cm) => "RNF191",
    qr(rrv194\d{4}cm) => "RNF196",
    qr(rrv195\d{4}cm) => "RNF200",
);
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Here's your code with tests. This does the actual search/replace as necessary as it converts @data to @output.

use strict;
use warnings;
use Test::More tests=>1;
use Data::Dumper;

my %Ren2Dol = (
    qr(rrv193\d{4}cm) => "RNF191",
    qr(rrv194\d{4}cm) => "RNF196",
    qr(rrv195\d{4}cm) => "RNF200",
);

my @data = qw(
    rrv1931009cm.new090626
    rrv1941009cm.new090626
    rrv1951009cm.new090626
    rrv1961009cm.new090626
    rrv1931234cm.new090626
);
my @expected = qw( 
    RNF191.new090626
    RNF196.new090626
    RNF200.new090626
    rrv1961009cm.new090626
    RNF191.new090626
);

my @output;
foreach (@data) {
    while( my( $regex, $replace ) = each (%Ren2Dol))
    {
        s/$regex/$replace/ex;
    }
    push @output, $_;
}

is_deeply( \@expected, \@output, "names updated correctly") or
    diag( Dumper{ expected=>\@expected, got=>\@output });
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