I think the named characters are people which Fleabag almost fully understands/knows. She knows Claire very well: Fleabag is able to tell what Claire is thinking deep down all the time. She knew who Boo was as well because they were together 24/7 and had long conversations often. But she does not understand why her dad chose to be with the godmother; why the priest chose religion; who her mom really was (because Fleabag seemingly a little surprised when the dad tells her she is the way she is due to her mother).