Why can't I connect to SQL server 2017 LocalDB shared instance?
Seems to be a bug in LocalDb v2017 and higher. I tested all available versions, starting from v2012 SP4. Up to and including v2016 SP2, the friendly share name "(localdb)\.\SHAREDNAME" is accepted in the connection request. When using v2017 or higher, the request always results in an "instance not found" error.

I've also observed that querying all installed LocalDb versions with sqllocaldb.exe v results in an error message for v2016 and higher:


  Windows API call "RegGetValueW" returned error code: 0.


Not sure whether this behavior might be linked to the original issue.



UPDATE

Applying the registry fix linked in the question solves the version query.

After some more digging, I think I may have discovered the cause for the connection failure. When SQLLocalDb up to v2016 is installed on the local machine, the share feature works as follows:

In the registry, a new key is created in Computer\HKEY_LOCAL_MACHINE\SOFTWARE\Microsoft\Microsoft SQL Server Local DB\Shared Instances\{SharedName}. This key contains a string value  InstanceName, which stores the pipe name, as visible in the following screenshot:



When the corresponding instance is started, it always picks this pipe name. The name stays persistent, i.e. when the instance is restarted, the pipe name is reused.

This logic is destroyed when LocalDb v2017 or higher is installed: When an instance with a shared name is started, the pipe name in the registry is ignored. Instead, a completely different pipe name appears when querying the instance via sqllocaldb i {instance}. 

This is probably also the reason why the connection can't be established, since the pipe names don't match. Editing the registry value to match the actual pipe name solves the issue, but only until the instance is restarted.