I have a simple script to rename some files 

#cls
cd e:\scripts\br
Get-ChildItem -Filter "13615*.pdf" -Recurse | Rename-Item -NewName {$_.name -replace '136150','0' }
Get-ChildItem -Filter "11111*.pdf" -Recurse | Rename-Item -NewName {$_.name -replace '111110','0' }
#Write-Output  -Recurse |  {$_.name}
if ( $_.name.contains("-01") -ne "True" ) {
 Get-ChildItem -Filter "*.1.pdf" -Recurse | Rename-Item -NewName {$_.name -replace '.1.pdf','-01x.1.pdf' }
 }
Write-Output Done

what i get when i run it is 

Done
PS E:\scripts\br> powershell.exe .\renamer.ps1
You cannot call a method on a null-valued expression.
At E:\scripts\br\renamer.ps1:6 char:6
+ if ( $_.name.contains("-01") -ne "True" ) {
+      ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    + CategoryInfo          : InvalidOperation: (:) [], RuntimeException
    + FullyQualifiedErrorId : InvokeMethodOnNull

so clearly $_name.contains("-01") isnt working the way I expect...any ideas on where I am going wrong?

if ( $name -match '01') {

You cannot use pipe variables because you have no pipeline.  What you are trying to do looks very confused.

We do not match with the string 'True' for truth value as this will fail in many cases so don't start a bad habit so soon.  The results of a test are always $true or $false and an "if" always succeeds when the value is $true.

$_ is null in your code. It is only valid in a pipeline.

Go back and rethink what you are doing.  Revue the learning materials.  If you still are confused than as a specific question.

OK what I am trying to do is get inside this recursion and before doing the replace 

Get-ChildItem -Filter "*.1.pdf" -Recurse | Rename-Item -NewName {$_.name -replace '.1.pdf','-01.1.pdf' }

check if the $_.name  has the characters "-01.1.pdf" in it 

It still doesn't make any sense but here it is:

Get-ChildItem -Filter "*.1.pdf" -Recurse | 
     Where{$_.Name -notmatch '-01.1.pdf'} |
     ForEach-Object{
          Rename-Item -NewName ($_.name -replace '.1.pdf','-01.1.pdf')
     }

You can also do this:

Get-ChildItem -Filter "*.1.pdf" -Exclude *-01.1.pdf -Recurse | 
     ForEach-Object{
          Rename-Item -NewName ($_.name -replace '.1.pdf','-01.1.pdf')
     }