Renaming Fonts to match Mac font face

Hi,
I recently moved from Mac to a PC. I used Helvetica Neue on daily basis (in my opinion the best font). I couldn’t lived without it on my PC, so I bought a few of the fonts. However the naming is different, therefore if I open a document that I have created on my Mac with that font on my PC, the font is not recognized.

Is there a way to change the name of the downloaded fonts so that they match the once on the Mac, it which case my documents will be compatible?

Regards

I use Windows 10, and there is no way to change the name of the font that I know of.