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.
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."