The father of 2 was in great spirits Wednesday night in West Hollywood -- showing off his kicks and his glistening pants while hopping into the back of his ride.

While all smiles, he's asked the million-dollar question: What's your new baby's name?? Check out his response ... sounds like the due date -- for the name -- is right around the corner.

As we reported, A$AP and Rihanna had their second kid on August 3 in L.A. -- while his name is under lock and key, we do know it starts with an "R." Remember, they named their first son RZA, so they've got a theme going.

You'll recall, Rihanna broke the pregnancy news to the world on one of the biggest stages in the world -- showing off her baby bump during her Super Bowl halftime performance, which dropped the jaws of millions of fans.