“UNDEFINED” url during upload

When uploading new file to the folder, the plugin changes its name (and url) to “undefined”.
A month ago everything was fine, every uploaded file was given its proper filename and the same name as the direct link.
And suddenly it is no more. Just “undefined”.
The name can be changed to any desired, but the direct links is always left as “undefined-[number]”, eg. undefined-97, udnefined-158.

I disabled all the recently downloaded plugins, I disabled and uninstalled Media Library as well, installing it form sratch.

And again. “Undefined”.

Yes, it still works properly – but leaves a mess when it comes to URLs.

WordPress Version: 4.9.1
PHP Version: 5.6.30
MySQL Version: 5.0.92
Web Server: Apache/2.2.31 (Unix) mod_ssl/2.2.31 OpenSSL/1.0.1e-fips Home URL: http://ursynow.org.pl

Active Theme:
– Newspaper 8.1.2

Active Plugins:
– Akismet Anti-Spam 4.0.2
– Attachment Taxonomies 1.1.1
– Contact Form 7 4.9.2
– FooBox Image Lightbox 1.2.34
– FooGallery 1.4.12
– Google Captcha (reCAPTCHA) by BestWebSoft 1.33
– MailPoet 3 (New) 3.3.2
– Media Library Folders for WordPress 4.0.9
– Post Types Order 1.9.3.5
– Shortcodes Ultimate 5.0.2
– tagDiv Composer 1.0
– UpdraftPlus – Backup/Restore 1.14.2
– WP Exclude From Homepage 1.1.3
– WP User Avatars 1.3.0

The page I need help with: [log in to see the link]