I don't know why people say Becerra. He's never held statewide office, probably not too well-known. A two-woman ticket is too risky, Bernie Sanders is really up and age and may not be in good physical shape to be VP for 4 (let alone years, and some (like Warren, Booker, and Brown) would cost Democrats a Senate seat. I'm guessing she'll pick Kaine, who would be her best bet.
I've never considered being well-known to be a very important qualifier for VP. Anyone picked to be VP becomes a household name within the week anyway, and it's not like a lot of Americans know who Tim Kaine or Sherrod Brown are outside of voters in their home states and heavily politically-aware people (who by and large already know who they're voting for).
Also I seriously don't get the hype for Kaine. It's get why people believe Clinton could pick him, but the man is incredibly bland.
He's ideologically compatible, has executive/legislative experience, chaired the DNC, speaks Spanish and won two statewide elections in a purple state. He basically checks the most boxes. In an election against Trump, especially against an extremely abrasive ticket like Trump/Christie or Trump/Gingrich, bland is sort of a good thing. He has the right resume to round out a "steady hands" ticket, which conventional wisdom says is her best defense against Trump.
Fair enough. But personally I believe Clinton's biggest obstacle won't be attracting independents, but voter enthusiasm. Elizabeth Warren inspires more enthusiasm among Democrats than almost any politician I've seen (I honestly believe that Warren could win a one-on-one primary with Clinton), and unlike Bernie she hasn't spent the last half a year locked in an passive-aggressive battle with Hillary.