"I do not know her name."
Translation:Její jméno já neznám.
Jméno is neuter. In the Accusative Singular, the adjective endings and the word endings are the same in both the nominative and in the Accusative.
You would add -ho to the end if the noun was masculine.
Jejího bratra neznáme. = We don't know her brother.
Chápeš? Do you understand?
It is more natural to use "vědět" for a subclause here:
I do not know, what here name is. Nevím, jak se jmenuje.
For a direct object "znát" is the natural verb to use.
In older, say 19th century, Czech the division was more fuzzy, but we do not consider it natural today.
Czech is not the only language to have this distinction, see https://www.livinglanguage.com/blog/2012/07/02/wissen-vs-kennen-to-know-in-german/
Grammatically there can't be a comma in "I don't know what her name is".
It would only work if you had a conjuctive adverb e.g. "Unfortunately, I don't know what her name is".
In Czech could you use "znát" for a subclause like " I don't know what her name is, she didn't tell me"? Or would you use "vědět"?