How about

use strict;
use warnings;

package Max;

use DBI qw( );

my $robi;
my $dbh;

sub import {
   my $class = shift;
   if (@_) {
      $robi = shift;
      $dbh = DBI->connect(
         "dbi:SQLite:dbname=$robi",
         "", "",
         { RaiseError => 1, AutoCommit => 1},
      );
   }
}

...

1;
[download]

use Max '...dbname...';
[download]

Or

use strict;
use warnings;

package Max;

use DBI qw( );

my $robi;
my $dbh;

sub init {
   (my $class, $robi) = @_;
   $dbh = DBI->connect(
      "dbi:SQLite:dbname=$robi",
      "", "",
      { RaiseError => 1, AutoCommit => 1},
   );
}

...

1;
[download]

use Max;
Max->init('...dbname...');
[download]