I said 'Martok trusts Worf' because I read in a different post that you don't need to change the order of the names in the Klingon sentence to the English sentence, but I got it wrong and the answer said 'Worf trusts Martok'. Is there a reason for switching the order of the names?
Yes. The object (the receiver of the action) must go before the verb. The subject (the doer of the action) must go after the noun. The grammar requires that these words go in a particular order. But let's say you have two objects connected by je ("and"). Those names could go in either order and it is up to the composer of the sentence to decide which name should come first. Then when you are translating, you should keep those two names in the order that the composer of the sentence chose. martaq ghawran je voq wo'rIv "Worf trusts Martok and Gowron."