One of the parent's names. Or two as done in some countries. One is more common afaik.

There is a trend towards using most rare last name as opposed to the more traditional name of parent of one particular gender

Belgium law is quite restrictive. Up until recently you were required to use the father's surname if known. You're now allowed to use either or both unless one parent is unknown, in which case you have to use the other.

Confirming. I think I know at least two friends who have chosen the least common last name even if it was hers. And I belong to what would often be described as a very conservative group ;-)

Both parent's last names.

Then what do their children take for last names? Each generation we have a doubling of name length?

  Gen 1: FirstName P1-LastName P2-LastName

  Gen 2: FirstName P1-P1-LastName P1-P2-LastName P2-P1-LastName P2-P2-LastName

  Gen 3: FirstName P1-P1-P1-LastName P1-P1-P2-LastName P1-P2-P1-LastName P1-P2-P2-LastName P2-P1-P1-LastName P2-P1-P2-LastName P2-P2-P1-LastName P2-P2-P2-LastName

and so on...

Spain has an interesting system here, a person born into a Spanish-speaking family is given a first name followed by two surnames, the first being the father's family name (or, more precisely, the surname he gained from his father) followed by the mother's family name (or, again more precisely, the surname she gained from her father).

Or in your example:

Gen X: FirstName P1-First-LastName P2-Second-LastName

In Quebec, it can be any combination but there's a limit of two last names to avoid that exact issue.

What is the problem with that? Hard disk space is getting cheaper. :P

In a few generations we're going to need to increase the database field size for last name.

That gets pretty long after a few generations.

You might know Pablo Diego José Francisco de Paula Juan Nepomuceno María de los Remedios Cipriano de la Santísima Trinidad Mártir Patricio Ruiz y Picasso under a shorter name...