How can I test that a variable is more than eight characters in PowerShell?

Use the length property of the [String] type:

if ($dbUserName.length -gt 8) {
    Write-Output "Please enter more than 8 characters."
    $dbUserName = Read-Host "Re-enter database username"
}

Please note that you have to use -gt instead of > in your if condition. PowerShell uses the following comparison operators to compare values and test conditions:

• -eq = equals (==)
• -ne = not equals (!=)
• -lt = less than (<)
• -gt = greater than (>)
• -le = less than or equals (<=)
• -ge = greater than or equals (>=)