General Delivery. Most post offices have pochta do vostrebovaniya, a "general delivery", where you can pick up mail from the post office. You can address mail to any "'post office" by using the correct postal code, street address, including the words "Pochta Do Vostrebovaniya" and your name.
American Express card holders can have mail sent to the American Express office.
Name:
C/O American Express
Sadovaya-Kudrinskaya ul., 21a
Moscow, Russia
Tel... 956-90-04
Tel... 956-90-05