These two names are the names of two Hachamim (sages) who converted to Judaism during a time of tremendous persecution against those who converted. They were given these unusual names to hide their identities from people who could hurt them. The names allude to the first, quote-unquote, gerim (converts): Avraham and Sarah, whose names were Avram and Sarai; eventually, a hei was added to their names, making them Avraham and Sarah. So both of these names allude to Avraham Avinu and Sarah: Ben Bag Bag in this Mishnah and Ben He He in the next Mishnah. In this Mishnah, Ben Bag Bag is the son of Bag Bag. Five and five is the gematria (numerical value) of Bet-Gimel (five), Bet-Gimel. So the son of Avraham and Sarah is what it's alluding to. And in the next Mishnah, Ben He He is also the son of five-five: the son of Avraham, who had a hei—the five numerical value added to his name—and the son of Sarah, who also had a hei added to her name.
Ben Bag Bag says, “Delve into it, delve into it again, because everything is within it.” Talking about the Torah: turn it over, turn it over; look at it from every single angle, every single side. Whatever you want is going to be found in the Torah. If you study in a very intense manner, you'll find all types of wisdoms, all types of Chokhmah (wisdoms). When you look at it from another perspective, you'll find another answer. The Torah contains an infinite amount of wisdom. And with it, you're going to see the truth. Whatever you're looking for, you'll find it within Torah. And grow old and get withered from it. Be busy studying from it, not only in your youth but throughout your life. Even when you get old, don't move away from it. Be busy studying it, no matter what. There's no point in time when you should say, “I have enough Torah in my life; I'm going to now go study Greek wisdom, Greek philosophy.”
You have no permission to study Greek philosophy, says the Gemara, except at a point when you're not allowed to study it—which would be in a bathroom or a bathhouse. They famously asked Rabbi Yehoshua, “What should I do? Should I teach my son Greek?” He told them, “Teach them at a time that's not day.” And that night, like the Pasuk (verse) says, you should ponder it, talking about the Torah, day and night. So, don't ever grow old from the Torah. And move away from it, and think that you've mastered it, and you want to go on to other wisdoms. Torah is something that we never finish with, because there's no better portion than the Torah.