[perl] Perl - Multiple condition if statement without duplicating code?

I don't recommend storing passwords in a script, but this is a way to what you indicate:

use 5.010;
my %user_table = ( tom => '123!', frank => '321!' );

say ( $user_table{ $name } eq $password ? 'You have gained access.'
    :                                     'Access denied!'
    );

Any time you want to enforce an association like this, it's a good idea to think of a table, and the most common form of table in Perl is the hash.