$page->set("status$de",1);
Sets the status for the $language (in my case $de).
$page->set("name$de", $this->sanitizer->pageName($pageName_de, [true]));
With "name$language" (in my case again $de) you set the Pagename in the Language.
I don't know if its best practice to set the default language (in my case $en) with:
$page->name = $this->sanitizer->pageName($pageName, [true]);
or
$page->set("name$en", $this->sanitizer->pageName($pageName_en, [true]));
I went with the first option, and did not try the second one. Depending on the language, I highly recommend setting up a small script, that converts language-related mutations ( you english people really call Umlaute 'mutations'?) to more machine-readable characters ("oe" for "ö").
PS: I really like the way processwire handles languages compared to other systems (I'm looking at you, WP!).
[Edit]: Somehow I posted the wrong link above and I am unable to retrieve the working one.
Dave Damage's post in Change Language Page Url was marked as the answer