FACE ID, which Apple filed on October 23rd, is for the stylized version of the name seen above. The application covers:
Computer hardware and software for secure biometric authentication, and password management and protection for use on computers, handheld mobile digital electronic devices and mobile telephonesin Class 9 and was filed on an intent-to-use basis (which suggests Apple is not using this as a trademark yet, but has a bona fide intention to do so in the near future - likely because pre-orders for the iPhone X didn't start until October 27th). Interestingly, Apple also claims a priority date of April 24, 2017 based on a trademark application it filed for this same mark in Liechtenstein. Claiming priority based on a foreign application is permitted under Section 44(d) of the Trademark Act. See also TMEP 1003.
Can Apple obtain a registration for FACE ID on the U.S. Patent and Trademark Office's Principal Register though? To obtain such a registration, Apple will need to show, among other things, that FACE ID is not merely descriptive of the listed hardware and software for secure biometric authentication.
A trademark is considered merely descriptive "if it describes an ingredient, quality, characteristic, function, feature, purpose, or use of the specified goods or services." TMEP 1209.01(b). For example, BED & BREAKFAST REGISTRY was held merely descriptive of lodging reservation services. In re Bed & Breakfast Registry, 229 USPQ 818 (Fed. Cir. 1986). Merely descriptive trademarks can be registered on the Principal Register if they become distinctive of the applicant's goods or services in the marketplace, but that is nearly impossible to show if a trademark was only recently adopted. TMEP 1212 et seq.
Assuming Apple obtains a registration for FACE ID on the Principal Register, it would have the exclusive, nationwide right to use that term in conjunction with computer hardware and software for secure biometric authentication (subject only to those who may have acquired trademarks rights in this term for the same or related goods prior to Apple's application). If it must amend this application to the Supplemental Register (which I call the minor leagues of trademark registrations) because the Trademark Office deems FACE ID merely descriptive, it would not obtain those exclusive, nationwide rights. TMEP 801.02(b); 15 USC 1094.
So, is FACE ID merely descriptive of computer hardware and software for secure biometric authentication? That will be up to the attorney at the Trademark Office assigned to this application (and perhaps eventually the Trademark Trial and Appeal Board and a federal court) to decide.
According to my quick search, this is the first trademark application for FACE ID filed by Apple and the 47th trademark application filed by the company in 2017.