A reCAPTCHA key is normally tied to a set of individual domains. However, if your list of valid domains is extremely long, fluid, or unknown, we give you the option to turn off the domain name checking on reCAPTCHA's end, and instead check on your server.
To do so, in the admin console, go to "Advanced Settings" for your key, and untick the "Domain Name Validation" box.
Turning off this protection by itself poses a large security risk - your key could be taken and used by anyone, as there are no restrictions as to the site it's on. For this reason, when verifying a solution, you are required to check the hostname field and reject any solutions that are coming from unexpected sources.