You should also check how many SQL Server instances are installed on the server and their names for non-default instances. To do this, we can use SQL Management Objects (SMO) with PowerShell and then use the ServerInstances member property:

#below should be a single line of code
$managedComputer = New-Object "Microsoft.SqlServer.Management.Smo.Wmi.ManagedComputer" $servername

#list SQL Server instances
$managedComputer.ServerInstances |
Select-Object Name, State, ServerProtocols, Urn |
Format-List

The preceding script simply lists the instances installed. Note that MSSQLSERVER is the name you'll see for a default instance: