#so the survival was always above any honor ideaological bullshit as if given a chance he would leave assassin life behind

[cienie-isengardu]

Names & titles (Such as Sub Zero) probably hold a deep importance in the Lin Kuei. Not having a title (Or having the title be stripped from you) is a fate more shameful than death.

Ages ago I did extensive analysis about Lin Kuei and one of the parts was focused on social hierarchy which said clan. My theory was that the code names are related to warrior’s mastery and in result, the determinant of social position. Of course, our knowledge and understanding of Lin Kuei’s inner matters is limited due to insufficient material but looking at cryomancers alone, we can say for sure the name of Sub-Zero carries a lot weight and even was the subject of the dispute between Kuai Liang and Bi-Han (Noob Saibot) or Kuai Liang and Frost. So I think we may agree it is a great honor for any cryomancer to have this title bestowed on them. At the same time, various source material mentioned that the Sub-Zero title is passed down between warriors and in case of Sub-Zero brothers, it was passed down in their family for at least three-four generations. So, I don’t think losing it per se is a fate more shameful than death, as if Lin Kuei cryomancer will be lucky enough to survive to their old age, it feels natural to assume the title will be passed down to much younger warrior to carry on the tradition, as this benefit the most the clan. However I would not exclude the possibility that one warrior may challenge another to usurp the title and in result get a better social position within the Lin Kuei social hierarchy. At the same time the conflict between Grandmaster Kuai Liang and Noob Saibot Bi-Han gives us some vague idea that stealing the code name or taking it after a dead family member without proving yours right to it, is a serious matter. One that would be punished harshly, as Lin Kuei does not tolerate pretenders. 

So in general, I agree with you that the code name holds a great importance within Lin Kuei structures and culture, however I’m not so sure if losing said title is seen as shameful, as the Sub-Zero title was traditionally passed from one generation to another for decades. Like yes, losing respected name will be an awful feeling no matter what and a big blow to warrior’s ego and there are probably cases where losing a title involves disgrace (and probably severe punishment) but if one could be challenged for the right to use a specific code name, maybe Lin Kuei had established a proper set of laws to keep everything under control and each potential candidate needed first prove their might to back their claim?

Also, it may be just me, but Noob doesn't sound ashamed for losing his title - only angry that Kuai Liang appropriated his "identity". Which says a lot about Bi-Han and though losing code name is A BIG DEAL, is not treated as something worse than death. But then, Bi-Han had always a different idea of "honor" than his younger brother.