There are several sites that offers services to register your URL to several search engines but I think that registering it to Google and to Bing, that are the biggest ones, is more than you need … and this can be done simply without using third party services that always ask you email and more.
Therefore to register an URL to Google search engine, you can go here.
To register in Bing you can go here.
After few click you’ll receive the following notification in both cases: “Your request was successfully submitted!”
You may need to wait few hour or days before you new URL will be registered, after a verification done by the search engine … from then on, it can be found searching it!