It's not a complete solution, more of a clue about which Org you are dealing with.
Have a look at the pod identifier. This is the forth character in the ID and comes straight after the 00D keyprefix.
With this you can determine the Pod/Server that the Org was created on (see important Caveat below). There is a separate question that lists how to do the mapping in more detail.
E.g. If the Org ID was 00DE00001234ooT, then the Pod identifier is E, which corresponds to NA9.
Probably the best information from this approach is if you are dealing with a Sandbox or a production Org.
The BIG problem with this approach is that it doesn't account for Orgs that are migrated from one Pod to another. This does occur and makes such an approach unpopular with a number of people. Use it as you will.
Pods also change over time, such as new ones being activated.
You may also want to look into the Environment Hub to manage multiple Organizations that you own:
The Environment Hub main page displays a list of all member organizations connected to the hub. For each organization, its
name, description, edition, organization ID, single sign-on status, and other details are displayed.
Or the License Management App for client orgs using a managed package.