Setting a Named Separation to "None" is a way of creating an ink should be ignored by the rendering application. This doesn't happen in PDFBox as it appears to use the CMYK representation when displaying the PDF in the debugger and when it creates a rendered png file.
BufferedImage bim = pdfRenderer.renderImageWithDPI(page, 300, ImageType.RGB);
Other applications (Acrobat, ImageMagick etc.) render the output correctly.
The attached PDF FIle illustrate this.
TwoCircles_NS.pdf was created in Adobe Illustrator and saved as PDF without compression. It uses a couple of named separations NS_1 and NS_2.
TwoCircles_NS-None.pdf is the same PDF content but the names of the name separations have both been set to "None" - This was done in a HexEditor but in practice it is done via PDFBox.
PDFBox_TwoCircles_NS-None.pdf-1.png is the result of the PDFBox Render to PNG which doesn't appear to follow the PDF Spec. and the definition of None when used as a named separation.
ImageMagic_TwoCircles_NS-none.png is the output from "magick convert -density 150" which appears to be correct/gives the desired result.