package Foo;

sub new {
    my $class    = shift;
    my $dbh      = ...
    my $subclass = "$class::$dbh->{Driver}{Name}";

    eval "use $subclass; 1;"
        or croak "$dbh->{Driver}{Name} is unsupported";
    
    bless { dbh => $dbh }, $subclass;
}

sub dbh {
    $_[0]->{dbh};
}