Thanks for stopping by the Apple Support Communities. From your post, I understand that you are trying to save a PDF onto your iPhone, using the "On My iPhone" option in the Files app. However, you do not see the On My iPhone option. I'd be happy to help!
In the Files app, "On My iPhone" does not appear until there is a file already saved locally. You can do that with the following steps from Use the Files app on your iPhone, iPad, and iPod touch - Apple Support :
Move iCloud Drive files
If you do not have anything in iCloud Drive yet, you can save your PDF to iCloud Drive, then move it to "On My iPhone". As long as it stays there, you will see that option the next time you try to save a PDF.
Cheers!