This is a fairly standard truthtellers-and-liars puzzle, with the twist that nobody is just a truthteller or a liar: the veracity of their statements depends on who they're talking to. Using this information, and the fact that for the purposes of this puzzle, love is a symmetric relation, you can figure out the couples:
Dorothy and DanieleIn each couple, the two people's names agree in exactly one letter, with exactly one first-agreement, one second-letter agreement, and so on. When sorted in this order (as above), the shared letters spell out DISCORD, the answer.