Not always, but mostly I do. Whether using named params:

my $obj = Module->new(log => $obj, arg1 => $arg1);
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or, positional (in this case, I typically have the log obj as the first parameter):

my $obj = Module->new($log, $arg1, $arg2);
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...and sometimes, I'll have the first arg as $self, then the log obj, then named params after that:

my $obj = Module->new($log, %args);
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The new() method would look something like this internally in that case:

sub new {
    my $self = shift;
    my $log_obj = shift;
    my %args = @_;
    
    # do stuff
}
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You can also call the class method within your new() method, and stash it inside the object:

sub new {
    my $self = bless {}, shift;
    $self->{log} = Library->log()->child('This::Module::Name');

    my $log = $self->_log()->child('new');
}
sub foo {
    my $self = shift;
    my $log = $self->_log()->child('foo');

    # do fooish type stuff
}
sub _log {
    return shift->{log};
}
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