Getting a website to show up in Google search or any other search engine, or rank first, is unfortunately fairly complicated and takes some time. It would be great if we, or anyone, could press a button or submit a form to make it happen right away, but that's not how it works.
Search engines like Google use an algorithm to determine how websites rankings for any given search term. For example, if I search for your name, from there, Google looks at all the pages on the Internet that are the most relevant relating to your name (mentions, links to your site, etc.) Those pages could include websites, news articles, blog posts, etc.
As a site like yours becomes more active, and thus more relevant to the algorithm, the ranking starts to improve. Given some time, the site could even start to show up on searches that don't involve the name, but for topics and terms it covers well. One of the most important things you can do is to have a site with the best content you can make.
That's an extremely basic overview of how Search Engine Optimization (SEO) works, but if you want to read about it further, I'd recommend starting with Moz's The Beginner's Guide To SEO.
Also, if you ever receive email from any companies telling you that you need to submit your site to search engines, especially if they want payment for that, or if they claim they can guarantee good search rankings without you having to do anything, those are scams. They can't make that happen, and you can ignore them.