I do not know why (and I do not have a strong opinion on this), but somehow this (relatively recent) tradition of naming units after people feels weird to me. I know we are already used to these units, but imagine the unit of mass was called Einstein instead of kilogram.
The Newton unit has been around since 1948. But that was hardly the first term to be named after someone: Watt has been used since 1882, Farad since 1881, Fahrenheit since 1776...
Note that the name of the unit is 'degrees Fahrenheit', but I agree - this could be something that started the tradition, which became stronger with new discoveries in physics and chemistry in 1800s.
I am sure Newton didn't name the unit of force after himself, so I would roughly place the invention of such possibility around early/mid nineteenth century, that is, about 200 years ago, which is when the research in such areas as electricity and magnetism, thermodynamics etc. was in full swing.
Reopening a plastic soda bottle.
From a web interactive I wrote: http://www.clarifyscience.info/part/ZoomB?v=A&p=CK6Ji&m=torq... (2014)