It is worth is to be careful in whom you approach in a large VC firm. Yes, it is all one big firm with shared economics — but partners are judged individually as well (no matter what anyone says) and sourcing and deal flow matter at all but a handful of firms.
What is definitely hard is to switch partners. I.e., while I have a meeting with Jason, but it’s Byron I really want as my partner. You can do this, but you have to have a lot of leverage. It creates drama. If you’re Jason’s best idea for this quarter / year, he may well not want Byron taking over the potential investment. And Byron may not want it if he doesn’t get credit for “sourcing” it.
The East Coast vs. West Coast thing isn’t that important specifically. Don’t worry about that per se.
But do pick the right partner to engage with. Getting a different one as your lead can be tough.
Most firms will tell you it’s all a partnership, but you are kinda of stuck with your champion partner if you choose them. At least, usually.