Branding Database?

I do things very similarly to @Ben M. I keep ASE (Adobe Swatch Exchange) swatches of client colors and all the assets in folders, which I manage with a digital asset manager. Those folders are all synced via Dropbox, so I can access all client assets from any device, even the Web on client's computer or tablet. As far as notes and details about the client and the assets, I keep the short info inside the metadata for the files themselves, which you can do in Bridge or Lightroom. More detailed branding notes notes I keep in Evernote. I also keep any PDF brand style guides for the client's assets inside Evernote.

Personally speaking I keep a master branding document and images folder for any client I work with.  I like to make sure that I have .eps or .ai files of logos, and especially a map of all colors and their corresponding values across the color scales (HEX, RGB, CMYK, PMS).  As for an app that does this, I don't have one. I have a Word doc that I re-use over and over with all of this information and use page navigation so everything is easy to find by page.

I suppose you could put that information on your Creative Cloud space in separate folders for each client.

CC Storage Space varies by Plan.

If you have a full Adobe Creative Cloud membership or a single app membership, you have 20 GB of storage. If you have a Creative Cloud Photography membership, a trial product, or a free membership, you have 2 GB of storage. Creative Cloud for teams and Creative Cloud for enterprise memberships include 100 GB of storage per seat.