Since I assume you don't have two databases with the same name, making them hash keys makes the test much easier.

#! /usr/bin/perl

use strict ;
use warnings ;
$|++ ;

my $DB = 0 ;
my %DB_list = map { $_ => 1 } qw( DB1 DB2 ) ;

until ( $DB_list{ $DB } ) {
    print "Select a database: " ;
    chomp( $DB = <STDIN> ) ;
    $DB = uc $DB ;
    if ( $DB eq 'Q' ) { print "Quitting...\n" and exit }
}

print "You chose $DB.\n" ;

__END__
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_______________
DamnDirtyApe

Those who know that they are profound strive for clarity. Those who
would like to seem profound to the crowd strive for obscurity.
            --Friedrich Nietzsche