When you run a site collection health check before upgrading to SharePoint 2013, SharePoint will check to see if there are any conflicts between existing content types and content types that are created when you upgrade the site to SharePoint 2013. A conflict occurs when both content types have the same name.
To fix this issue, you need to rename the existing content type before upgrading. For the steps to rename an existing content type, see Create or customize a content type.
