To add a new search engine in your Matomo (Piwik) server, you can use the ReferrerManager plugin which lets you manage Search Engines and Social networks.
The lists of Search engines and Social networks detected by Matomo are maintained in our searchengine-and-social-list project on github.
Since Matomo 2.16.0 definitions are automatically updated in Matomo installations using a scheduled task. This guarantees your Matomo uses the latest definitions.
You can read more about how to add/edit a search engine or social network definition in the README file of the repository.
(Matomo uses an icon for each search engine and social network, placed in the directory plugins/Referrers/images/)