Basically, [I've been corrected on
Lang-8](http://lang-8.com/1175392/journals/89388753240708953573691087311691779178/%25E7%25A7%2581%25E3%2581%25AE%25E3%2581%25AA%25E3%2581%25BE%25E3%2581%2588%25E3%2580%2582?t=correction#journal_comment_217368597129492706286705882073422302314)
that [あなたの名前はですか] should be changed to [なんというお名前ですか], or [あなたの名前何といいますか].

After a quick search around, I found that なんという means how as in [how
[beautiful]]. I figured that this is a polite way of addressing the second-
person, but this still leaves me a little confused on the proper way to ask
for second-person's name. [何といい] didn't register as a word at all in a online
dictionary I've used, and some other members have said that [あなたの名前はですか] is
completely fine!

Could someone demystify this mess please?
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grammar questions
The use of なんというお名前ですか?
What you wrote is grammatically not correct. So far you have

> あなたの名前  
>  your name
>
> は  
>  [topic particle] (not to be translated in English)
>
> です  
>  [copula] is
>
> か  
>  [question particle] ?

In other words, what you wrote translates to

> あなたの名前はですか  
>  [big unfilled gap] is your name?

You want to fill the gap with "what", in Japanese 何{なん} to give you

> あなたの名前は **何** ですか  
>  **What** is your name?

The other way suggested to you means something like

> あなたの名前は何と **いいます** か  
>  _How do you **say** your name?_ or _How do you **call** your name?_

That said, what you said might work on an internet forum, but in face-to-face
conversation the more common way to say "What is your name?" is お名前は何ですか.
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Your sentence, あなたの名前はですか、 is both grammatically incorrect and rather rude
(once fixed) as well. As Earthling said, to make it grammatically correct, you
need to add [何]{なん} → 名前は何ですか

The impolite part is the use of the pronoun あなた; Japanese learners are best to
avoid this word -- as well as other second-person pronouns -- until they know
when to use it and when not to use it.

Typical ways of asking for somebody's name are:

> お[名前]{なまえ}は？
>
> お名前は[何]{なん}ですか。
>
> お名前は[何]{なん}と[言]{い}いますか。

Note that I'm using お名前 rather than 名前 or あなたの名前; the お prefix makes the word
'honorific', which in practice means that the word translates to **'your
name'.**

* * *

On second thought, it is fine to use あなた in a blog (?) post like that, when
you are talking to a reader in a one-way conversation. Textbooks use it all
the time. Most learners, however, aren't writing one-way conversations, so the
common advice still stands.

(I assume lang-8 is closer to a blog than to a forum.)
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なんという is the plain form of なんといいます.

if taken literally, it means "how is it said"

so it's like saying "how is your name said?"
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