The verb is not at the end because this is a question, not a statement. In all questions, the verb appears much earlier in the sentence.
Also, while SOV (subject object verb) is the most common syntax in Latin, "esse/to be" is a copula, not an active verb. As such, it takes a complement rather than an object. SVC (subject verb complement) is quite common as it helps disambiguate subject from complement.
"Why exactly is not the verb at the end?"
-SOV is most common, but it's not mandatory
-Here, it's a question. The verbs in question are closer from the beginning of the sentence, usually. (for instance Quid est...)
-When the verb is "to be", (a copula), it is found more usually in the middle of the sentence (or sometimes at the beginning).
You should read this entry regarding the use of "quod nomen" against "quid nomen". https://www.textkit.com/greek-latin-forum/viewtopic.php?t=62864
the dative here is used as a dative of possession :)
latin does this sometimes*: you could see a sentence like "the book is for/to you" (liber tibi est) instead of "the book is yours" (liber tuus est). a sentence like that with a dative of possession essentially means "you have the book"
*I'm not exactly sure how common the dative of possession actually is in latin :/ or if it's more common than just using a genitive. but I've seen it quite often :)
"What is X to you?" is asking the personal connotations and values you associate with something. Although it can also literally mean "How do you personally define X?" and shades of meaning in between. It depends on what X is.
For example, imagine a child's drawing. Now imagine you're showing it to someone and you ask "What is this to you?" Possible responses include:
"It is nothing to me." (Meaning they have never seen it before and for all they care you can throw it away.)
"I did that when I was five years old."
"My daughter made that when she was four." (If the person gently takes the paper from you and looks at it with a soft smile, this thing has sentimental value to them. They are probably going to keep it somewhere safe.)
It can also literally mean "Tell me your definition of X." For example, "What is love to you?" might be answered with "Love is accepting a person as they are and valuing their happiness."
So "What is a name to you?" is something like "What value do you put on a name? How much do names matter to you? How do you use names in everyday life?" It's somewhat practical, somewhat philosophical.
What I think he means is that while an educated speaker (i.e. one familiar with Greek) would most likely have consciously aspirated the t in a word like thema, Latin itself did not systematically have word pairs with different meanings distinguishable only by the presence or absence of aspiration -- in other words, the t / t(h) difference was not phonemic (as, say, the unvoiced t / voiced d distinction would be in English: tip versus dip).
That the tibi in the exercise is pronounced with an aspirated t has to do, I think, with the fact that the sentence is read out by a speaker whose first language is English, one in which aspiration of initial t is part of the regular sound system. Had the speaker been, say, French, Spanish, or Russian the initial t would almost certainly not have had this quality.
Probably because that's not how the Romans would say it, even if the way they say it sounds strange to us. In fact, a lot of sources give slightly different word order ("Quid est nomen tibi?", "Quid tibi nomen est") but are more or less the same phrase. It means "What name do you have?" if that makes it any easier.