Your website will be appearing in search results for what is unique about it (which may, at first, only be your name) shortly after publishing, but it won’t immediately be in the top results for more general descriptions of what you do.
It takes a lot of work over time to move up in the search results for phrases that relate equally to other individuals and companies whose websites are well-established.
Search engines will track users’ engagement with your website over time, however, and when their robots detect that users are interested in your content, your search engine results will improve.
Your best bet is to optimize your website for the most specific and relevant terms you can. A very good practice is to optimize your website for the kinds of questions you expect people to be entering in the search field if they are likely to be interested in what you do. To some extent you can do this by experimenting with searches but you can also use the data about what people actually search for. There are tools for this and we can help get your search engine optimization focused.