"What is your name?"
Translation:Quid tibi est nomen?
"Tibi" is not really the possessive "your", it's closer to "to you". So "Quid tibi est nomen" is not separating a noun phrase but rather "What to you is (the) name?"
Although Latin is primarily SOV, the word order is relatively flexible. Also, "esse/to be" is a stative/copular verb and as such does not take an object but rather a subject complement, meaning everything is in the nominative. Therefore it is common to see SVC as a way to disambiguate it from SV.
Havingf done translation work for over 30 years in Warlpiri, an Aboriginal language of Central Australia, it is very interesting to now be learning some Latin, another 'free' word order language. I put 'free' in quotes in that my experience in Warlpiri is that various word orders serve various pragmatic choices made by speakers to make certain things salient.
Is "nomen tibi quid est" wrong? In Portuguese you can say "teu nome, qual é?" and in Spanish I think "tu nombre, ¿cual es?" would also be acceptable, although definitely not common. Latin is way more flexible than those two, so it'd be weird to me if the sentence above were wrong.
Between grammatical number and gender and case declension, there are a lot of ways to form the possessive "your".
"Tibi" and "vobis" are the dative case. "Nomen tibi" is more literally "the name to you".
Here is a plain-English overview of what the cases are and how they work:
Latin cases, in English
Adjectives must agree in gender, number, and case with the nouns they modify, but they have their own declensions. Sometimes you get lucky and the adjective just happens to follow the same declension as the noun, but that is not a guarantee.
Back to a word order question.
We are asked to translate "Quid est ei nomen?" - what is his name.
Then we are asked to translate what is your name. I go for 'Quid est tibi nomen?' which seems to be following the same stucture to me. While my answer is accepted it offers "Quid tibi est nomen?" as an alternative, presumably the preferred alternative.
When does the thing word go between 'is name' and when does it go outside. Is it completely arbitrary and I'm reading more into this than I should? Is it 'mihi nomen est' or 'nomen mihi est' when I attempt to introduce myself?
It's extra flexible because that's the dative, not the genitive. "Quid est ei nomen?" is literally "What is to him the name?" That makes it easier to split up and move around.
Introducing yourself, as far as I've seen, would be "Nomen mihi est Heather", literally "The name to me is Heather".
"Quid tibi est nomen?" makes use of what is called the dative of possession. It makes perfect sense grammatically. Latin is not English and English is not Latin. Irish does something very similar.
Here, "Marcus" is in the nominative because it's either the subject or the subject complement: Nomen tibi Marcus est; Marcus est tibi nomen. Marcus is your name; Your name is Marcus.
It's the vocative "Marce" when you're addressing him directly: Marce, quis es? The address is not part of the sentence itself. Marcus, who are you?
So you would say "Marce, estne nomen tibi Marcus?"