Some will, some won’t. Some people get their own number.
For example, monks will give titles to their disciples, including lay disciples.
For example, some Taoists do not know how to get married, because some Taoists can marry wives, have children, and eat meat, so some families have no names. For example, the Quanzhen Seven Sons.
For those in the world of martial arts, if the apprentice already has a name, he will not take it, but this depends on the master's mood.