www.thespacereview.com/article/1215/2

We didn’t do many mission-type patches in Star Trek: The Next Generation, mainly because I didn’t want to be in a position where we had to come up with a new badge every time we ran into a new ship. A few years later, when we did Star Trek: Enterprise, the producers wanted a more NASA-like vibe, so I did quite a few emblems for Bob Blackman, our costume designer. Wendy Drapanas, Geoff Mandel, and Alan Kobayashi also contributed some patches.

This listicle says it was Wendy Drapanas but there’s no further explanation.