I was rewatching some lore videos about 'The Last of Us' recently, and this question about Ellie's last name actually popped into my head too! From what I've gathered through the games and supplemental material, her full name isn't explicitly stated. Joel never calls her anything other than 'Ellie' or 'kid,' and even official documents in-game just use her first name. It's kinda interesting how they keep it ambiguous—maybe to emphasize how her identity is more about her relationships than lineage.
That said, fans have speculated endlessly. Some think it might be Williams, since that's her mother's maiden name in the 'American Dreams' comic, but others argue she wouldn’t necessarily share it. Personally, I like the mystery—it adds to her character’s everygirl vibe. If they ever reveal it in Part III, though, I’d lose my mind!