Here's how I managed to do this with my solution in Visual Studio 2015:
Close your solution> go to .sln-folder> .vs (hidden)> config

Look for error prone names (possible multiples) in the sites section. I deleted every <site></site>one where there were naming conflicts. In my case, I had this, for example:
After deleting sections <site></site>from the current applicationhost.config file, I was able to re-add website projects with my new and correct name!
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