These particular names have separate canon English spellings and Klingon ones. Because the Klingon writing system you're learning mirrors the pIqaD script, what you're really doing is learning to represent the name in the Latin and pIqaD alphabets, akin to having to write Olga in English and Ольга in Russian if you do the Russian course. But more like writing Ol'ga, if ' represents the myadki znak (something that probably has a proper English spelling that I don't know).
Personally I hate having to remember how Paramount spells these names in English, and would like for the course to accept either the Klingon or English spelling in either direction, so I know exactly where you're coming from.
Duolingo is encouraging all courses to use the same spelling in both languages when they use the same character set. We really should be adding the Klingon versions as accepted answers in English translations. But we have not put much effort into it yet.
Qov, feel free to add the "Klingon spelling" to the ATs. But let's keep the "English spelling" as BT, so learners can begin to recognize them when they see them outside of this course.