"the Klingon's name"
The Duolingo computer system creates those "wrong" answers and recapitalizes them (always capitalizing the first letter and removing capitals from the other letters). And just as bad, in those exercises where the contributors create the "wrong" answers, it does the opposite and leaves the "wrong" answers as is, but recapitalizes the right answer. In any case, tlhIngan 'oHba' would mean "It is obviously Klingon."
I suppose we could be creative and come up with a circumstance where we are talking about "a Klingon" or "the Klingon" even though the pronoun is 'oH. But since we don't seem to be talking about a being I would be much more likely to interpret the tlhIngan adjectivally. I'm actually not fully certain that sentence is grammatical either. Do we have precedence for a sentence like tlhIngan 'oH Duj'e' or does it have to be tlhIngan Duj 'oH Duj'e'?