I had the same challenge one time. For the sake of others that may have the the same challenge:
Remember to use your canonical URL when using site:example.net
http://www.example.com
is different from http://example.net
In your Google Search Console, remember to add your both variants of your domain name and monitor their search status.
However, your canonical URL is more important.
Wondering what your canonical is?
It is the variant of your site that you choose to display in search results.
It helps to prevent duplicate content in search results.
It is usually specified by the link tag in the head section of your page, as follows:
<link rel="canonical" content="www.example.net"/>