Explanation/Reference:
Conflicting content types were found during site collection health check 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.