More about this in chapter 46. Mild spoilers, she has no idea what being in a relationship means and thinks of him as her guardian. He obviously likes her, but, being a Japanese male, refuses to act on that and vehemently denies they're in any sort of romantic relationship. It's unexplained so far whether she's using his last name to pretend they're married for legal reasons or to pretend she's an overseas relative or whatever. But it's the sort of detail this manga usually eventually fills in!