Setting a global PowerShell variable from a function where the global variable name is a variable passed to the function

You can use the Set-Variable cmdlet. Passing $global:var3 sends the value of $var3, which is not what you want. You want to send the name.

$global:var1 = $null

function foo ($a, $b, $varName)
{
   Set-Variable -Name $varName -Value ($a + $b) -Scope Global
}

foo 1 2 var1

This is not very good programming practice, though. Below would be much more straightforward, and less likely to introduce bugs later:

$global:var1 = $null

function ComputeNewValue ($a, $b)
{
   $a + $b
}

$global:var1 = ComputeNewValue 1 2