Yes, you can switch Grand Companies. Your ranking and points will be reset to zero for your whichever Grand Company you go into, although you will retain your rank for your current Grand Company if you ever switch back. There is also a fee and timelock associated with it, depending on your rank, so you can't switch too often.

I can't remember who you speak to to leave your current GC, though.

Edit: I'm pretty sure you lose all yours seals, as well.