If you believe your old site does not have much SEO value and a rebranding of your company would help, I believe it would be a good idea to go ahead. However, you mentioned that you plan on going into social media and content marketing. In that case, roidirectmail.com may not be a good representation of the services you are offering? roisolutions.com or the original site name sounds like a better representation to me.
Even if your old site does not have much search traffic, you should consider doing a 301 redirect of your old site to the new site. You would want any possible visitors to your old site to be redirected to your new site, and not be lost in a sea of 404 pages.
