You can switch from one brand (or generic) to another immediately if you choose; you don't even have to finish your current pack if you don't want to. You can just start the new birth control when you receive it. As long as you have no days off between your last pill of the old brand and your first pill of the new brand, your pregnancy protection will be maintained without interruption if you switch mid-pack. You may be more likely to experience spotting or breakthrough bleeding with this method.
Should you choose to finish your current pack of birth control, that is also OK! You'll just start the new pack the day you would have been due to start your next pack of the old brand - that is, the day after your last placebo pill from the old pack.