Hi Chris
usually names kind of 'emerge' by concensus in solar physics. The first
person to observe a phenomenon might dream up a name, and if the name
fits then other people use it and it sticks. If it is not a good
description then it disappears and is replaced by something else. To my
knowledge there is no organisation that decides what name something
has, unlike for new asteroids, for example. Sometimes words become
over-used, such as the word 'filament', which has at least three, and
possibly four, different meanings in solar physics.
The name 'umbra' means 'shadow', from Latin as you maybe know.
'Penumbra' means 'almost the umbra'. My Oxford English Dictionary tells
me that 'umbra' was in use for sunspots since at least 1788, and in
1860 and 1868 was used by the astronomers Olmsted and Lockyer
respectively.
However, since Latin was the language of science for hundreds of years,
anyone from Galileo onwards could have been the first to use the name!
Or maybe even before, but as Galileo had made telescope observations of
the sun in 1611, he would have been able to see the umbra and penumbra
clearly.