Some characters have random traits, others don't?

[Cetan]

Example:
Count Sigfus of Vestisland, Iceland has the same fixed five traits every time you start September 15, 1066
Duke Conan II of Brittany has a random trait every time you start the same date.

Is this working as designed?

 

[Veldmaarschalk]

Example:
Count Sigfus of Vestisland, Iceland has the same fixed five traits every time you start September 15, 1066
Duke Conan II of Brittany has a random trait every time you start the same date.

Is this working as designed?

Yes, this is WAD.

Most characters converted from CK1 have kept their traits (like Sigtus). Edited characters (like Conan II) from CK1 and newly created characters from CK2 (unless they were really famous) have received no traits, the game will automatically generate them.