I need to create a copy of a Windows Store app that will coexist with the original one on the store. I plan to create a copy of the solution folder and then change the package display name in appxmanifest (Packaging).
Is there anything else I need to change to prevent conflicts between the apps?
Changing the package display name won't be sufficient and even it's not needed - you can have two apps with the same name on your phone. The most important is Name (in Identity node) and PhoneProductId (in PoneIdentity node) - they must be different for each app. You won't edit them easily by opening packageappx.manifest file by double click, instead right click on the file, choose View code and edit mentioned data:
<Identity Name="SmthFromStoreWithLittleChange" Publisher="CN=something" Version="1.0.0.0" />
<mp:PhoneIdentity PhoneProductId="082abc73-hereAlsoLittleChange-ea7ea4735fbd" PhonePublisherId="any GUID here" />
Remember that each of this apps has its own LocalData folder (LocalSettins and other data also).