Add-LocalGroupMember does not work properly


I reduced the code sniplet I am reffering to to some lines:

$UserName         = "A6-R306TN97"
$UserPassword     = "depp"
$UserPasswordEnc  = $UserPassword | ConvertTo-SecureString -AsPlainText -Force
New-LocalUser -Name $UserName -Password $UserPasswordEnc
Add-LocalGroupMember -Member $UserName -Group Benutzer

We are having about 450 PCs for students and since a long time, the computername is the same as the local username.

When I add a user to the machine with the script above, the user is added, but it is not visible in the user Access control.
We found out (via computermanagement -> compmgmt.msc), that the user is not Show als a member of the Group “Users”.

Although: When I do retype the Add-LocalGroupMember line it says, that it is already there.
Adding Users with the same username as the machine Name in the UAC works fine.

Any idea?

Forgot to mention: OS is Win 7 64bit.