Assuming they actually do have a passport, the link you mention tells you exactly what to do here.
Expanding on what that links is saying though:
Any passport they have should be an ICAO 9303 (or, alternatively, ISO/IEC 7501-1, which is the same thing) compliant machine-readable travel document, which means it has this covered.
In particular, on all ICAO 9303 compliant documents, there is a machine readable zone (MRZ) consisting of two or three lines of text in the OCR-B font. In a standard passport booklet, this is at the bottom of the identity page. On most passport cards, it’s on the bottom of the reverse face of the card.
The MRZ includes the name of the document-holder, either as the entirety of the third line if there are three lines, or as everything from the sixth character of the first line to the end of the first line if there are two lines. Some special rules get used when constructing this (punctuation other than hyphens is not included, hyphens and spaces are replaced with
< (the filler character used in all parts of the MRZ), most diacritical marks are removed, and specific transliteration rules are used when dealing with non-Latin alphabets), but the contents of that particular field in the MRZ should pretty much always be acceptable to an airline as a passenger name when booking a flight.
In cases where you can’t use a full name, the name as listed in the MRZ on whatever travel document you will be using is almost always the correct thing to use.