Yes, 301 redirect old page names to new relevant ones. If you have almost no non brand ranks, then don't overthink it but do the redirects. Then as always look at your bad links using variety of tools and compile all the links. Review each one because some with low authority may be ok and visa versa. Google Search Console is where you upload the dissavow file to turn bad links "off". Then check the new site for duplicate content. Start adding more in depth pages and blog posts including great content worth linking to and email people who link to similar content to promote it along with Facebook boosts.

How did your relaunch go?