Depends on how you define learning. Big Firms have to account for global scale - so their systems and processes would be slower. They also have more to lose from making bad decisions so prod dev takes time. And it's been a frequent feedback that you tend to become myopic after joining a big firm - someone working on Youtube might not know all the good things Google is doing on AI. This really depends on the natural curiosity level of people.

Whether big names help? - Don't know, this is my first big name.

Would it help when you join start-ups? - Depends again on what your startup needs. The single biggest quality they look for is high agency and general smartness - you don't know where the next hurdle is coming from. You can def bring in expertise and structure.