One of the weird side effects of clones is that they, somehow, share memories on occasion, even if the clone didn't get memory-flashed, as was the case with Giuseppe and Peppino. As a result, Peppino will occasionally get flashes of "memory" from Giuseppe's life, and vice-versa. The phenomenon has gotten attention as the truth of clones has been explored. It's assumed to be something related to just how alike a clone and their original are genetically - like the universe itself occasionally has trouble telling them apart. It also seems to get stronger with proximity.
In Fake's case, they did receive some of Peppino's DNA during their - for lack of a better term - creation. As a result, they occasionally get these memory flashes, too, but they're more subtle. They realized it was happening when they greeted someone they'd never met before and knew things about them they shouldn't have known. The memories had just implanted themselves in their brain without preamble or fanfare. Despite it only happening a couple of times, Fake finds this incredibly disturbing. They worry that someday enough of Peppino/Giuseppe might sneak in to essentially make them a True Clone of one or both of them.
This won't happen; with five different personalities, there's now almost always one watching for such things. But the idea of being essentially overwritten - even by someone they consider a friend - for someone who suffered such a horrible identity crisis once already - is terrifying.