It might not be the same for you, but for me, worrying about fonts for the dissertation was a classic sign of self-distraction!
Your university probably has strict formatting requirements for dissertations, which may rule out choosing your own font. Certainly, any publisher will require your article to use their journal's font.
Ultimately, in most academic settings, you can only control the fonts you use to write privately, or the fonts you use if you put anything up on a personal website. Whether you steal the fonts you use to write privately is, I suppose up to you, but I recommend against it.
Stealing fonts to display your work publically is a really bad idea, for the reasons the other answers go into. Also (as a thought experiment) because you'd be rightly annoyed if a font designer grabbed pages of your dissertation to use as the sample text advertising their typography without crediting you, and so fair is fair.
To answer your question about trying to identify a font found in the wild, this page has some good resources:
Good luck with the diss!