There can be a problem in the order in which names are written - forename and surname. (This problem faces all teachers of English as a Foreign Language.) The problem is: how should one write the student's name? The problem is made worse by the use of computers.
In Britain, our most usual habit is to say or write the surname last - e.g. "Christopher Columbus", "John F. Kennedy", "Tony Blair", the great boxer "Muhammad Ali" (who began as "Cassius Clay") and "David Beckham". In these cases, the forename - obviously - comes first. In some circumstances, mostly bureaucratic or official, as in the military forces or in such lists as those of students in a class, it is written first. In these cases, it is written with a comma after it - "Columbus, Christopher", "Kennedy, John F.", "Blair, Tony", "Ali, Muhammad" and "Beckham, David".) This usage, surname first, is the most convenient for alphabetical lists like lists of students, Bibliographies, catalogues and so on. It is also the easiest for computers to handle.
The problem is caused by the fact that in many other societies it is usual to say the surname first, and then add the personal name. (So first name has become a misleading word.) Such non-native students are advised to say clearly "My surname is XXX; my forename is YYY." That should be clear. Also, the term surname is clearer to many native Britons than family name, which is not recommended in use with native speakers.