Can someone with HSV1 acquire HSV2 by giving oral sex?
The reason they are usually known as oral (HSV1) and genital (HSV2) herpes are that the majority of genital herpes cases used to be from HSV2. However, this has been changing and now HSV1 is the more dominant genital infection at least in some regions. Moreover, people can be infected by both, even in the same "region", though it's unlikely that most people even know whether they are infected by HSV1 or HSV2 because testing what strain someone is infected with not always done, from what I understand. So yes, someone with HSV1 can additionally acquire HSV2, both orally and genitally.
In addition to that, even a genital infection with HSV2 may lead to shedding the virus from the oral region - it is uncommon, though.