Use the same line, just add the "-ComputerName".

This:

Get-WmiObject win32_service | where {$_.DisplayName -match "SQL Server"} | select Name, DisplayName, State, StartName

Equates to this for running it on my local machine:

Get-WmiObject win32_service -ComputerName localhost | where {$_.DisplayName -match "SQL Server"} | select Name, DisplayName, State, StartName

You use the same command and pipeline commands, just adjusting for running it remotely. So your command would just be:

Get-Service -ComputerName $ComputerName -Name SQL* | select Name, DisplayName, State, StartName