There are 2 problems when using a fake name
Problem 1
You might not be able to pay with a card due to your bank security policy.
Problem 2
You might not receive the package, depending on how your local post service works.
Also, if the package will get lost you cannot open dispute with post.
Solution:
The package and billing statement is discreet, so you should not worry. However, if you still would like to take extra privacy measures we suggest using PO box or parcel lockers