As a general rule, just like in English, people think it's more polite if you can say the same sentence using more (meaningless) words.
For example, you can ask a person's name by
- Could you tell me your name?
and the former is generally considered more polite.
The same goes here for Korean,
- 이름이 뭐야? (to someone in lower status/standing)
- 이름이 뭡니까? (in a formal, businesslike situation)
- 이름이 어떻게 되세요? (pretty polite)
- 이름이 어떻게 되시는지요? (even more polite)
되(-다) verb here is very light, carrying almost no meaning (like verb
Also note that the bottom two sound quite awkward, since to the nouns (
이름) do not correspond to the level of politeness from the verbs.
존함 would be okay, as in OP's example.
Lastly, some argue that
이름(성함)이 어떻게 되세요(되시는지요)? is ungrammatical, since here the speaker raises the name of the listener (the subject of the sentence), not the actual person. The point is that you must use
-시- honorific tail only with human subject. From this perspective, you should ask
이름이 어떻게 돼요(됩니까)? Still, a lot of people use
-시- with a person's property in real life, especially in CS/CRM industry.