My question may not be related with English language. It might be more of correct usage.
Which one of the following is correct?
Your name, please?
Your good name, please?
// as if there is a bad name.
From Text Types and the History of English (Manfred Görlach, 2004)...
One of the best-known modern parodies [of Indian English] is R. Parthasarathy's “What is your good name, please?” which makes fun of almost all the features in which IndE deviates from the proclaimed British model, such as (apart from the localising function of of names):
1) tense and aspect confusion
2) irregllar use of articles
3) invariable tags (isn 't it? no?)
4) questions marked by intonation only
5) pleonastic uses (headache pain, discussing about)
6) local idioms (inter-caste, matric fail, foreign-returned, put up) and wrong uses of BrE idioms (make the two ends meet)
7) erudite diction (eschew, opine, purchase)
I won't include the full text of the parody here (it's in both the above links), but obviously the implication of the title is that this usage is archetypally IE (it's totally "normal" to speakers of IE, but totally "weird" to most other Anglophones). But the list of other IE features is useful to know.
Regarding the specific insertion of good in OP's example, it's worth noting this from Bilingualism in Schools and Society (Sarah J. Shin, 2013)...
Politeness in Indian society is highly conventionalized and is part of the conversational style of Indian English. The strategy of maintaining a positive face can be seen in the example: What is your good name, please?
...and this from Art And Science Of Translation (Centre of Advanced Study in Linguistics, Osmania University and Booklinks Corporation, 1994)...
In a Hindi situation with a high degree of formality, one would tend to ask: H. apka subh nam (kya hai)? The items in parenthesis may or may not be used. This is translated very frequently in English in India as : E. What is your good name?
It seems this is a direct translation of the Hindi “Aap ka shubh naam?” But even Google didn´t return too many results, so I would take it with a grain of salt.
The first one is “correct” in the sense that it is very likely to be understood by anybody with basic English usage. And as others have pointed out, a formal version of that would be “Your name good sir?”, although I suspect that is archaic by now.
After living in the UK for some time as a non-native English speaker, I have never heard anyone use either “Your name good sir?” or “Your good name, please?”