How to correctly mention people in a PhD thesis?
Generally you should ask your advisor on that. It strongly depends on the discipline and probably the requirements of your parent institution. For example in my case the correct method was Method X was invented by Doe, but I have written a few works where the citation style was customarily Method X was invented by J. Doe as well as Method X was invented by John Doe.

On the other hand I can't remember any paper where an author would introduce biographical data of the people whose names are referred. You are generally not writing about those people but their ideas. Moreover, sometimes you may be unable to find the birth and death dates - what would you do in that case? Omit the data in case of few people where you were unable to find it?