I'm not sure if there is a command for it: I have never found one.
Deletion: However, you can use the web interface to Wolfram Data Drop to manage your databins, including renaming them and removing any of them entirely. The direct link to the administration page is the following:
Here is a link to the user guide for the Wolfram Data Drop that mentions databin administration functions, where you can see that one of the possible actions is deleting the databin (the thrash an icon):
Renaming: If you click on any databin in the "My Databins" page, it will open an info page on the specific databin. Click on its name and it will allow you to change it.
The name is considered one of the options of a
Databin object, so you can also use the following to change the name of an existing
SetOptions[DataBin[yourdatabinID], "Name" -> "A nice new name"]
In my understanding, however, the name property cannot be used to refer to the databin directly, or at least I haven't found a way to do it.