Use lc to lower case the words used as keys for the lookup hash and lower case the search text. The code already finds long protein names which have a prefix that is the same as a shorter protein's name. I've added a splice to avoid finding a short protein that matches a part of the long protein name that has just been found. Oh, and I updated the print to generate the desired output.

use strict;
use warnings;

my $sentence = 'a long mixed case name protein is found in preference 
+to a mixed case name protein which is found before a short protein';

my %proteinLU;

while (<DATA>) {
    chomp;

    my $protein = $_;
    my @parts = split;
    my $parent = \%proteinLU;

    while (@parts) {
        my $part = lc shift @parts;

        $parent = $parent->{$part} ||= {};
        next if @parts;
        $parent->{_name_} = $protein;
    }
}

my @words = map {lc} split ' ', $sentence;

while (@words) {
    my $word = shift @words;

    if (! exists $proteinLU{$word}) {
        print "$word ";
        next;
    }

    my $parent = $proteinLU{$word};
    my $wIndex = 0;

    while ($wIndex < @words && exists $parent->{$words[$wIndex]}) {
        $parent = $parent->{$words[$wIndex++]}
    }

    print "**$parent->{_name_}** " if exists $parent->{_name_};
    splice @words, 0, $wIndex;
}


__DATA__
long Mixed Case name protein
Mixed Case name protein
Protein
[download]

Prints:

a **long Mixed Case name protein** is found in preference to a **Mixed
+ Case name protein** which is found before a short **Protein**
[download]

Hi, I notice a problem which does not tag short protein name and some words in the sentence are missing. But I don't know what is wrong in the script. I extracted the protein names which contains word "MCM2" and the test sentence which has problem. Is the problem related to redundancy in the protein names with different case? Thanks for any information!

use strict;
use warnings;

my $sentence = 'Protein kinase A-anchoring protein AKAP95 interacts wi
+th MCM2 , a regulator of DNA replication';

my %proteinLU;

while (<DATA>) {
    chomp;

    my $protein = $_;
    my @parts = split;
    my $parent = \%proteinLU;

    while (@parts) {
        my $part = lc shift @parts;

        $parent = $parent->{$part} ||= {};
        next if @parts;
        $parent->{_name_} = $protein;
    }
}

my @words = map {lc} split ' ', $sentence;

while (@words) {
    my $word = shift @words;

    if (! exists $proteinLU{$word}) {
        print "$word ";
        next;
    }

    my $parent = $proteinLU{$word};
    my $wIndex = 0;

    while ($wIndex < @words && exists $parent->{$words[$wIndex]}) {
        $parent = $parent->{$words[$wIndex++]}
    }

    print "**$parent->{_name_}** " if exists $parent->{_name_};
    splice @words, 0, $wIndex;
}


__DATA__
replication licensing factor MCM2/3/5-type protein
replication licensing factor MCM2 ALT_NAMES:MCM2p
replication licensing factor MCM2 ALT_NAMES:CDCL1
minichromosome maintenance protein MCM2 homolog
minichromosome maintenance protein MCM2
DNA replication licensing factor Mcm2
DNA replication licensing factor mcm2
DNA REPLICATION LICENSING FACTOR MCM2
mcm2 DNA replication licensing factor
Mcm2 DNA replication licensing factor
DNA replication licensing factor MCM2
contains MCM2/3/5 family signature
Central kinetochore subunit MCM22
replication licensing factor MCM2
Central kinetochore subunit MCM21
Similarity to yeast mcm2 protein
similarity to yeast mcm2 protein
MCM2/3/5 family , most YBR1441
novel MCM2/3/5 family member
NOVEL MCM2/3/5 FAMILY MEMBER
budding yeast MCM2 homolog
member of MCM2/3/5 family
MCM complex subunit Mcm2
MCM2/3/5 family protein
MCM2-related protein
At5g18020/MCM23_11
At5g18030/MCM23_13
mcm2-prov protein
MCM2 , FORMERLY
MCM2/3/5 family
P1 clone:MCM23
mcm2 protein
Mcm2 protein
MCM2 protein
mcm2-prov
MCM23_15
MCM23_13
MCM23.13
MCM23.11
MCM23.15
MCM23.16
MCM23_14
MCM23_16
MCM23.14
MCM23_11
MCM23_7
Mcm2-PA
MCM23.9
MCM23.6
MCM23_4
Mcm2-RA
MCM23.7
Mcm2-XP
Mcm2-XR
MCM23.4
MCM23_6
MCM23_1
MCM23_3
MCM23.3
MCM23.1
MCM23_2
MCM23.5
MCM23_9
MCM23_5
MCM23.2
mcm22p
mcm2_1
Mcm22p
mcm2_2
Mcm21p
mcm21p
MCM2_1
huMCM2
DmMcm2
MCM2_2
DmMCM2
X.MCM2
hMCM2
dMCM2
mcm22
MCM21
mMCM2
xMCM2
MCM2p
MCM22
mcm2p
mMcm2
mcm21
MMCM2
MCM2
mcm2
Mcm2
[download]

Desired output will be:

Protein kinase A-anchoring protein AKAP95 interacts with **MCM2** , a 
+regulator of DNA replication.
[download]

Replace:

    my $parent = $proteinLU{$word};
    my $wIndex = 0;

    while ($wIndex < @words && exists $parent->{$words[$wIndex]}) {
        $parent = $parent->{$words[$wIndex++]}
    }

    print "**$parent->{_name_}** " if exists $parent->{_name_};
    splice @words, 0, $wIndex;
[download]

with:

    my $parent = $proteinLU{$word};
    my $wIndex = 0;
    my @best;

    while ($wIndex < @words && exists $parent->{$words[$wIndex]}) {
        @best = ($parent->{_name_}, $wIndex) if exists $parent->{_name
+_};
        $parent = $parent->{$words[$wIndex++]};
    }

    if (@best) {
        print "**$best[0]** ";
        splice @words, 0, $best[1];
    } else {
        print "$word ";
    }
[download]

There was no fall back to the longest match so far if a longer partial match existed. In the sample case 'MCM2' was being masked by 'MCM2 , FORMERLY'.

There is no need (but no major harm) to provide different case versions of the same match string unless you want to use a case sensitive match with only the given variants allowed (in which case you need to remove lc in the various places it is used).

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True laziness is hard work