I prefer having a variable too. I'd even do

  our $Customer = My::Company::Namespace::Customer::; # <--- trailing 
+colons!
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to make sure that I didn't mistype the class name. (See Re: Capitalized subroutine names and packages.)

Variables has the extra advantage of expanding right:

  # Hi, this is written by me, the maintainer.
  do_something_with_class(Customer => \&callback);
  # Oops, I missed that Customer really was a
  # subroutine mimicing a bareword. *That* took a
  # while to figure out, huh!
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Generally, I don't like to make stuff look like something it isn't.

ihb