ComputerNamePhysicalNetBIOS and "Current Host Server" shows different machines
Windows Server Failover Clustering requires a minimum of two computers (Virtual Machines or Physical Machines).  Lets refer to these as Node01 and Node02.
Part of the install process for the Windows Server Failover Clustering role defines the name of the cluster.  For our purposes let's call that MyCluster.
Once you have created MyCluster, you can add SQL Server instances to the cluster as independent &quot;cluster resource groups&quot;.  We'll refer to our SQL Server clustered instance as MyClusterSQL\INSTANCE.
So, to clarify, we have:
╔════════════════════════╦═══════════════════════╗
║          Item          ║         Names         ║
╠════════════════════════╬═══════════════════════╣
║ Computers              ║ Node01 and Node02     ║
║ Cluster Virtual Server ║ MyCluster             ║
║ SQL Server Instance    ║ MyClusterSQL\INSTANCE ║
╚════════════════════════╩═══════════════════════╝
Now, if you run SELECT SERVERPROPERTY('ComputerNamePhysicalNetbios') it will return either Node01 or Node02 depending on which computer is hosting the SQL Server Instance.
SELECT SERVERPROPERTY('MachineName'); will return MyClusterSQL.  The Microsoft Docs for SERVERPROPERTY says this about &quot;MachineName&quot;:

Windows computer name on which the server instance is running.
For a clustered instance, an instance of SQL Server running on a virtual server on Microsoft Cluster Service, it returns the name of the virtual server.

SELECT @@SERVERNAME; will return MyClusterSQL\INSTANCE.
Server Manager always returns the name of the computer you connect to.  In our case, this will be either Node01 or Node02.  If the SQL Server Clustered Instance is running on Node02, and you connect to it using Remote Desktop to the MyClusterSQL server, Server Manager will show Node02, even though you connected to MyClusterSQL.