It is not really clear what you are trying to achieve here. Your variable naming convention really does not make it clear what the desired output is.
You do some undefined check on $user_name and put the results in $no_name which you do not use. You push the city value into an array but try to print as a scalar, perhaps a hash of arrays is not the appropriate data structure to use.

Here is a slightly modified version of your code that uses a check_name sub and correctly displays the array contents. Hopefully this gives you a clue as to how to modify your code to achieve your goal.

use strict;
use warnings;

my $result = data();

foreach my $key ( keys %$result ) {
        my $value = join(',', @{$result->{$key}});
        print "User Name = $key - City: $value\n";
}


sub data {

    #db code stuff
    my $sql = [
                { username => 'abc', city=> 'foo' },
                { username => 'def', city=> 'bar' },
                { username => 'ghi', city=> 'goo' },
                { username => 'jkl', city=> 'car' },
                { username => 'm-n-o', city=> 'car' },
                ];
    #...
    my %no_name_found;
    if ( @$sql ) {

        for ( @$sql ) {
            my $user_name = $_->{'username'};
            my $city = $_->{'city'}  || '';

            if ( check_name( $user_name ) ) {
                push @{ $no_name_found{ $user_name } }, $city;
            }
        }

    }
    return \%no_name_found;
}

sub check_name {
    my $name = shift;
    if ( $name =~ /^\w+$/ ) {
        return $name;
    }
}

Output
User Name = def - City: bar,bas
User Name = abc - City: foo
User Name = jkl - City: car
User Name = ghi - City: goo
[download]

If you still are having problems please provide a more detailed description of what you are trying to achieve, include all relevant subs and a sample of input data and how you want it to display on output.