To use your site in with multiple domains, you've need to set multiple Google API key for each domain with www and without www.

You can do this at the configuration of the plugin. Go to Mambots, submenu Site Mambot and click on Google Maps. Then you can enter the Google Multi API key.
Enter it as <website>;<key>.

Website should be without http://.
Each combination should be on a new line.

My site works for tech.reumer.net or tech.reumer.eu.

For example:
tech.reumer.net;AGAJGAGA.....
tech.reumer.eu;ASUIOJSJLKS....
www.reumer.net;JKLJLK890HKH....
reumer.net;HKJHKKY922JLJO....

In the configuration of the plugin you can use two possibilities for the domain name. The configuration item Url variable can use HTTP_HOST of PHP or Config for the Joomla variable. HTTP_HOST is used when using subdirectories on your main domain (for example: tech.reumer.net/beta) so you can register the key for the main domain (tech.reumer.net).

If the keys are not accepted then turn on debug of the plugin. Reload the page with the message that the key isn't allright. Show the source of the page and look in the debug messages if the url and the configuration can match.