Hi Alexandra,
I think the name comes from the fact that if you look along the edge of the Sun the prominences stick out - they are "prominent" so they were called "prominences."
This is true particularly in a special kind of red light produced by hydrogen atoms in the Sun's atmosphere. It is very common for telescopes on the ground to observe prominences in this kind of light.
Here is an example from the Pic du Midi H-alpha coronagraph in France:
http://bass2000.bagn.obs-mip.fr/New2003/Pages/Instruments/pr010927.064412.gif
cheers,
Terry