Iterate over the array and extract the prefixes. Use the prefixes as hash keys and push the filenames onto a hash-of-lists:

my @array = qw(001.file.a 001.file.b 002.file.a 002.file.b) ;

my %groups;
for my $filename ( @array ) {
    my $prefix = (split /\./, $filename)[0];
    push @{ $groups{$prefix} }, $filename;
}

for ( keys %groups ) {
    print "group $_ has files @{ $groups{$_} }\n"
}
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Output:

group 002 has files 002.file.a 002.file.b
group 001 has files 001.file.a 001.file.b
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