"Její jméno já neznám."

Translation: I do not know her name.

[blublevita]

Does the "já" here serve the purpose of emphasis?

[ValaCZE]

Yes it is because of emphasize "já".

[unci14]

Would the word order "Já neznám její jméno" also be possible?

[BossKaiden]

I think that if you did that you would basically be saying, "I know her, but not her name." Since you're putting emphasis on "jméno".

[dalila747]

Is it normal to always have the verb at the end? It seems all the examples in this unit are like this but I don't see an explanation.

[Jamie08MD]

It's definitely not a rule. These sentences often emphasize the verb and show that there is more than one possible word order. However, when using short sentences, there are not many options where you can place the verb, so it often ends up being the last word even for neutral sentences.

Speaking specifically about this sentence (ie. including the personal pronoun), the verb is emphasized.

A neutral sentences would be "Já neznám její jméno." or "Její jméno neznám."

[Janmunroe]

Would Jeji jmeno be acc. sing. neuter here? My brain is clogging up at the moment.

[VladaFu]

yes

[Vlad_Lesnievski]

As I understand
"I do not know its name" and "I do not know their name" would be legitimate translations as well, wouldn't they?

[VladaFu]

Certainly not their (jejich). Perhaps "its" if we consider a not-living entity that is feminine in Czech. But it certainly is feminine here.