I'd use BrowserUk's approach of having a thread pool and feeding jobs to that pool through a queue. Each thread then returns its results to the main program again through a queue.

You can easily turn your serial program into such a queue-based program after you have a working serial program. You haven't made clear that your existing program already works as a single-threaded program, so I can't give you much working code, but given your vague outline above, I'd use something like this:

#!perl -w
use strict;
use threads;

my $THREADS = 20;
my $request = Thread::Queue->new;
my $response = Thread::Queue->new;

my %dataEntity = (
    ...
);

# Submit all requests
for my $dbname (keys %dataEntity) {
    $request->enqueue([ $dbname, $dataEntity{ $dbname } ]);
};

# Tell each thread that we're done
for (1..$THREADS) {
    $request->enqueue( undef );
};

# Launch our threads
for (1..$THREADS) {
    async(\&getData);
};

sub getData {
    while (my $job = $request->dequeue()) {
        my ($dbname, $credentials) = @$job;
        # connect to DB, retrieve information
        $response->enqueue( "Results from $dbname" );
    };
    # tell our main thread we're done
    $response->enqueue( undef );
};

while (my $payload = $response->dequeue or $THREADS--) {
    print Dumper $payload;
};
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