Updating a 5 year old site with bad SERP and DA of 1. Should I change the domain?

The site is for a small business. It has been around for 5 years and only gets 300 users a month. It doesn't have an SSL certificate and it's not using http2. It hasn't broken any spam rules. Could it be flagged for anything that would impact the effectiveness of doing SEO? Can I work with the existing domain or am I better off getting a new one? It's currently the business name, but I was considering making it one of the client's keywords if I have to change it.