fix my website name not showing on google search engine

My site is built entirely with custom HTML + CSS, yet when I type the brand name into Google nothing relevant shows up. I’m looking for someone who can diagnose why the pages aren’t being displayed correctly and then implement the technical SEO fixes that will get the proper name and title to appear in the search results.

What I expect: an initial audit of the current markup, robots and canonical settings, creation or correction of meta titles, descriptions, structured data and sitemap, submission through Google Search Console, and any server-side tweaks needed so that Google can crawl and index the site without obstacles. Once the changes are live, I’d like a short verification report confirming that Google has re-indexed the pages and that the brand name is now showing.

Please be comfortable working directly in plain HTML/CSS, using standard SEO tools, and explaining your steps so I can maintain the solution going forward.