I wouldn't count on a fake name being any kind of problem for facebook assuming they're actively using the profile. Not providing them any data at all won't spare you, but if you're using the account they can easily analyze photos and comments (including those on other people's profiles), use facial recognition, use friend/activity patterns, match IP addresses/browsers (including any instances where the same IP address/browser was used to sign into non-facebook services found in records purchased by facebook from data brokers), and if he ever uses his phone or chrome to look at facebook there's a handy unique ID sent to facebook as well which can be matched with countless other recorded activities.

Facebook devotes a huge amount of time and money to collecting data and using it to associate people to a real identity to the extent that even people who never signed up for an account at all have hidden profiles created for them by facebook which contain the intimate details of their life including what they buy at the grocery store.

As far as I can tell, a container won't protect your identity but it will limit the amount of information they have on your browsing history (unless your ISP decides to sell them that information or they obtain some of it from a 3rd party data broker)