if ($identnr =~m/^\d[*]$/)

if($identnr =~ /^\d+\*$/)

....
                elsif ($identnr =~ /^\d+\*$/)  {
                        suchen_wild()
                }
.....

sub suchen_wild {
        my $dbh = DBI->connect($DBN,$DBUSER,$DBPASS) or die $DBI::errstr;

        my $statement_suchen="SELECT * FROM $TABELLE where ident_nr like '$identnr%'";
        my $sth_suchen=$dbh->prepare($statement_suchen) or die $DBI::errstr;
......

sub sterne_entferne {
    my $mit_sternen = shift;
    ( my $ohne_sterne = $mit_sternen ) =~ s/\*//g;
    return $ohne_sterne;
}

use strict;
use warnings;

my $foo = "Hello world!\n";

print $foo;

&print_foo;

print $foo;

sub print_foo {
    print $foo;
    $foo = "Hello perlworld!\n";
}