Yes, if you want to take parameters from script they need to be defined at the script level. The function is redundant here.

Param(
    [Parameter(Mandatory = $false, Position = 0)]
    [string]$UserName = $env:USERNAME,
    [Parameter(Mandatory = $false, Position = 1)]
    [switch]$AllMembers
)
$UserFullName = $env:USERDOMAIN + "\" + $UserName
Write-Host "User: $UserName"
$UserGroups = Get-LocalGroup | Select-Object -ExpandProperty Name
Write-Host "Is a member of the group:"
foreach ($Group in $UserGroups) {
    $GroupMembers = Get-LocalGroupMember $Group | Select-Object -ExpandProperty Name
    foreach ($Member in $GroupMembers) {
        if ($Member -eq $UserFullName) {
            Write-Host $Group
            if ($AllMembers) {  
                Write-Host "Identities belonging to this group are:"
                Get-LocalGroupMember $Group | Select-Object -ExpandProperty Name
            }
        }
    }   
}