When a site is new, little is known about it. Google likes to test new pages and sites with higher positions for a period. There are two thoughts on the subject. One is that any good site should enjoy testing for a period instead of falling to the bottom of the SERPs and never being able to compete. The other thought is that while a sites metrics are being built, and this takes quite a bit of time, any site should be given some grace.
All sites will perform well for a period. That is well known. However, as a sites metrics are gathered in the index and SERP performance metrics are gathered, SERP placement begins to change to something more appropriate.
Another consideration is how the site performs in the SERPs for specific search queries. Any site will vary in how it can be found by specific search queries. Since about 15% of search queries are new and have never been seen before, that vast majority of search queries are well known and sites that perform well for these queries are well established and difficult to compete against. It may be that your site will perform well. As well, it may be that your site will not perform well. Time will tell.
So while your new site is performing well today, that may be only for a period and for select queries to be adjusted over time. If branding is what your goal is, I suggest focusing on that. This answer How do you get Google to show wiki information about your site in the right side bar of the search results? talks about some of the steps in branding.