Remove matching issues when files are compared to a text list

I took the liberty of using your long lists of files and 'movielist.txt' from your previous question, because in there it shows there are lots of extra characters in the names that complicate things..
Not only the (year) in the desired names, but also some files have dots instead of spaces in their names, non-ascii hyphens (en-dashes) etc.

To do what you want you will need to

• create a title Hashtable to store the actual value from the movielist.tst file as value, but also have a cleaned-up version of that to do the comparison with
• extend each FileInfo object in the files array with an extra property (I call 'SearchName') that stores a cleaned-up version of the actual file's BaseName to compare against.

$titles = Get-Content -Path 'D:\Test\movielist.txt' -Encoding UTF8 | Select-Object -Unique
# first create a Hashtable with searchable (cleaned-up) titles and the actual title you want as filename
$titleMap = @{}
foreach ($title in $titles) {
    # remove everything after a square bracket, remove the year in between brackets, 
    # remove all non-ascii characters and trim trailing spaces
    $search = ($title -replace '(\(\d{4}\)|\[.*|\s*)$' -replace '[^\x00-\x7F]+' -replace '\.|\s+', ' ').Trim()
    $titleMap[$search] = $title
}

# next, get an array of these search titels, sorted on Length reversed
# to avoid bad renames on ambiguous names like 'Il cavaliere oscuro' and 'Il cavaliere oscuro - Il ritorno'
$searchTitles = $titleMap.Keys | Sort-Object Length -Descending


# get the list of files in the foler
$files = Get-ChildItem -LiteralPath 'D:\Test' -File -Exclude 'movielist.txt'
foreach ($file in $files) {
    $search = ($file.BaseName -replace '(\(\d{4}\)|\[.*|\s*)$' -replace '[^\x00-\x7F]+' -replace '\.|\s+', ' ').Trim()
    # extend each object with a cleaned-up searchable name
    $file | Add-Member -MemberType NoteProperty -Name 'SearchName' -Value $search
}

# now loop through the search titles and try to find matching filenames from the files
foreach ($title in $searchTitles) {
    $files | Where-Object { $_.SearchName -like "*$title*" } | ForEach-Object {
        # use '-ErrorAction SilentlyContinue' to avoid errors on files that have already been renamed
        Rename-Item -LiteralPath $_.FullName -NewName ('{0}{1}' -f $titleMap[$title], $_.Extension) -ErrorAction SilentlyContinue
    }
}

• Title from movietext.txt says Highlander 2 – Il ritorno (1990), but filename is just Highlander 2 1080p.mkv. To have a match, you also need Highlander 2 in your movietext file.
• Title from movietext.txt says Halloween 2 – Il signore della morte (1981), but filename is Halloween 2 - Il Signore Della Morte.avi. Here again, in the text file you use an En-Dash instead of a normal hyphen.
• Title from movietext.txt says Heartbreakers – Vizio di famiglia (2001) which has an En-dash instead of the normal hyphen the filename Heartbreakers - Vizio di famiglia.avi, has, so they don't match.

Maybe, because you seem to create the movietext.txt in a word editor like Word that automatically uses typographic glyphs instead of straight characters, a better solution would be to use a helper function on top of the script:

function Get-ComparableName ([string]$Name) {
    $Name -replace '(\(\d{4}\)|\[.*|\s*)$' -replace                          # remove anything after (and including) a square open bracket and the year in brackets
                   '\.|\s+', ' ' -creplace                                   # replace dots into spaces and normalize spaces
                   '[\u201C\u201D\u201E\u201F\u2033\u2036]', '"' -creplace   # replace double-quote glyphs into straight quotes
                   "[\u2018\u2019\u201A\u201B\u2032\u2035]", "'" -replace    # replace single-quote glyphs into straight quotes
                   '[\p{Pd}\u2212]','-'  -replace                            # replace dash-like glyphs into a straight hyphen
                   '([^\x00-\x7F]|\p{Cf})+'                                  # remove non-ascii and invisible control characters
}

and use it like:

foreach ($title in $titles) {
    $search = (Get-ComparableName $title).Trim()
    $titleMap[$search] = $title
}

and a bit further down:

foreach ($file in $files) {
    $search = (Get-ComparableName $file.BaseName).Trim()
    # extend each object with a cleaned-up searchable name
    $file | Add-Member -MemberType NoteProperty -Name 'SearchName' -Value $search
}

As for the file Highlander 2 1080p.mkv, you need to add a title Highlander 2 (1990) in your movielist.txt file, otherwise it will not be matched..

No fancy regex here other than making an array of movie names and years

$filmTextList = @()
get-content -path $rootFolder\movielist.txt | %{$filmTextList += [PSCustomObject]@{Name=($_ -split "(\(\d{4}\))")[0];Year=($_ -split "(\(\d{4}\))")[1]}}

$filmFiles = get-childitem -path C:\Users\Peter\Desktop\test skript\test1
foreach ($film in $filmTextList){
    try{
    $matchedFilm = Get-Item ([WildcardPattern]::Escape($filmFiles.FullName -match $film.Name))
    Rename-Item -LiteralPath $matchedFilm.FullName -NewName "$($film.Name) $($film.Year)$($matchedFilm.Extension)" -ErrorAction SilentlyContinue
    }catch{}
}

Otherwise here's a working version of your 2nd attempt:

$rootFolder = "C:\Users\Peter\Desktop\test skript\test1"
$files      = Get-ChildItem -Path $rootFolder -File
$filmTextList = @()
get-content -path $rootFolder\movielist.txt | %{$filmTextList += [PSCustomObject]@{Name=($_ -split "(\(\d{4}\))")[0];Year=($_ -split "(\(\d{4}\))")[1]}}
foreach ($film in $filmTextList) 
{
    $files | Where-Object {
        $_.BaseName -match $film.name
    } | ForEach-Object {
        $ext = $_.Extension
        Rename-Item -LiteralPath $_.FullName -NewName "$($film.name)$($film.year)$ext" -EA 0
    }
}