If you want to avoid namespace clashes, you can just avoid the method lookup entirely and pass the object as the first parameter to the private method (this happens anyway, we just aren't faking it). As a bonus, the subroutine lookup time is reduced:

my $private1 = sub { print "Private1\n" };
sub _private2      { print "Private2\n" }

sub public_method 
{
    my $self = shift;
    $private1->($self);
    _private2($self);
}
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Calling like this shouldn't be done for public and protected methods because it breaks subclassing, but private methods aren't supposed to be subclassed anyway.