my $sql = "select login from login where login like ?";
# (I would have used different names for table and column)

my $sth = $dbh->prepare( $sql );

my $newname = "whatever";

$sth->execute( $newname.'%' );
my $likenames = $sth->fetchall_arrayref;

# update: remembered that fetchall_arrayref returns AoA,
# so added map to get actual field values into grep
# (also remembered to include the "execute" step above)

if ( grep /^\Q$newname\E$/, map { $$_[0] } @$likenames ) {
    $newname .= "00";
    while ( grep /^\Q$newname\E$/, map { $$_[0] } @$likenames ) {
        $newname++;
    }
}