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Normally you define the CM at the project level. Then within a package you add a "reference" to the CM. Within this reference you can parameterize the connection string. So this is doable at the package level.
But what I might start with is setting your project CM's connection string to have application name portion of the string use the PackageName system variable. I'm not sure it'll pass validation at the project level. If that doesn't work then you'll need to instead make that change inside the package's CM properties.