Yes, there are more than just Google in SEO.
But, well, I don’t want to go after stats and data to find which search engines are worthy to work with, but in ball park figure, Google owns it and Bing is the next contender. There are International search engines like Yandex, Baidoo that are strong in non English world.
Both Google and Bing provide services for site owners, to manage sitemaps and search engine friendliness etc.
If you are working with Google, see Google Search Console
If you are working with Bing, see Bing Webmaster
I recommend, after publishing your website, sign into these services and verify your site ownership. Get recommendations from their services.
Here are my list
|Name||Url||Share % in the US*|
Not engines but popular search media powered by other search engines