That can be tough. What might be some strategies to rank for that alone, despite ranking for other stuff? Anyway, your site needs enough SEO juice for ranking for your own site name at least. Anyone agrees?
Its not gonna be an easy journey moving to the top search engine but if you can be able to generate traffic for your blog or site, by advertising it on other sites, there are also sites where you can upload tasks for people to visit your site and then you pay them a Little token for their work. This are among the ways you can generate traffic to be on the top search engine.
More content will help with getting your name to the top, along with a few other things like keywords (having keywords that contain your site name, for example), meta descriptions, and of course traffic.