In Bleach, there are Four Noble Families of the Soul Society. I know that people can have children in the Soul Society. However, is whether you are a part of the Noble family based on whether you were born into that family in the real world or in the Soul Society? For example, if you are from the original line of the Kuchiki family (in the real world) and you died, would you become part of the Noble Family?
I do not think they went deeper into the noble houses, so I believe there is no current information available about "How to become a noble". All the currently available information on the 4 noble houses can be found here.
There they also state:
The Noble Houses of Soul Society have an unclear role in the culture, social and governmental aspects of that dimensions existence.
Some speculation from my side: I think that they were either appointed by the Soul King or the Central 46. And I also believe the divisions are involved in this.
There is reason to believe that the captaincy of the 6th Division runs in the Kuchiki family, as at least two members, both of them were family heads, have held the title captain and two other known members have been lieutenant and 3rd seat respectively.
This part is just speculation though.