It looks like you modifed an existing project before the database rename was added. If you'll notice, the error indicates that the MDF file could not be overwritten:AVSQLDSN.mdf
Make sure that the data file in all of your FileGroups begin with the $DbName$ so that the MDF changes with the database renames.
If you are going to support multiple instances on the same server, then you MUST have dynamic file group names as well.