Name for a part on stands/trainers
In the manuals/parts lists I have seen, Schwinn and Blackburn refer to the part that envelopes the ends of the axle or quick-release skewer as a "cone". Minoura refers to it as a "grommet" at the end of a "coupling".

I don't have a Cyclops manual handy. I also don't think there is an industry standard name for this part, as there is some variation between all manufacturers when it comes to the coupling/mounting mechanism of their trainers.