According to some reaserch: ABBA of Abba Shaul was a title, not part of his name.
TWO names is a relatively new thing. I don’t think you’ll find any Tanna or Amora with more than one name, but if I am wrong, I will accept.
No one really has TWO NAMES. A person has A name: ויקרא שמו בישראל, HIS NAME, not NAMES. Even someone who has multiple names, all those names are ONE name: Rav Shach zt”l had one name: ELAZAR MENACHEM MAN. If someone were to name his son after Rav Shach zt”l just “Elazar” he didn’t give him Rav Shach’s name. He gave a name to his son, something that will remind him of Rav Shach – but that is not his name. Similarly if a person is given two names, after two people, he is really not named after either of them, rather he has his own NEW name.
That is my understanding. But I may be wrong. כך מקובלני מבית אבא.