Here's how I would have presented this question, with an SSCCE:

use strict;
use warnings;

use Test::More;

my @good = (
        'aa1.2',
        'aa1_bb2'
);

my @bad = (
        'aa1_2',
        'aa1_2bb',
        '1aa'
);

my $re = qr/^[a-z][^_]*(_[a-z].*)?$/;

plan tests => @good + @bad;

for my $str (@good) {
        like ($str, $re, "$str matched");
}
for my $str (@bad) {
        unlike ($str, $re, "$str not matched");
}
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Note that this is a working solution as well as a statement of the problem. See also How to ask better questions using Test::More and sample data.