I've recently worked on improving my ranking by increasing my backlinks...but if all my backlinks show a www, should I change my domain name to include www? Its been a naked domain for 3 years.

Will changing it to include the www hurt my SEO more than help it at this point? According to moz my naked domain's search visibility is at 1.04% and the domain authority is a 9. Any insight on this would be greatly appreciated!!!! I'm all out of marbles on this one.