I think that now I see what you are trying to do.
If you really don't like to use the hostname \ instance combination and you use your own SQL client to connect, you can always add an alias to your own client, called local, which resolves your instance. This way, you can save your connection string in your application the same way no matter which server / instance you end up inserting into the application, simply by changing the alias.
See the link below for more details on customization:
How to configure and use a SQL Server alias
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