I think you answered your own question..it sounds like you are waiting for DNS...other databases will be the same if they are using the same host. If you have a host that currently works, and the new database is on the same machine, just use the other hostname (they are interchangeable). Otherwise, you won't be able to get at them with PhpMyAdmin until the host DNS updates. The time it takes varies greatly, and depends on a lot of things, including your own computer's cache, possibly your ISP's DNS, and even your router sometimes caches DNS. Actually, because of this, trying too soon only makes it worse.
To see it as soon as possible, clear all your caches, reset your router, and give it some time before trying again...In my experience at least 30 minutes. Patience, Grasshooper, Patience!