Amateur astronomer fag here. Not sure if it's been figured out yet but the constellation (if it is a constellation) on the left looks like Delphinus to me. The star pattern on the right….I have no idea.
Also consider that these could asterisms and not defined constellations. It's also possible they could be ancient constellations that are not recognized by modern astronomers. Since this pertains to US Space Force, it would be my guess that these star patterns are likely patterns that can be seen from the Northern Hemisphere were the USA is as opposed to Southern Hemisphere star patterns.
It's also possible, even likely, that the star patterns depicted will not perfectly match any star charts due to "artistic license".
I believe that most military patches/logos generally have some paperwork attached at creation that clearly spells out each part of a design and what it represents. I'm not sure where you would find such info but I was involved in designing one as a Boy Scout decades ago and there was a bunch of paperwork involved for submission of design, approval, adoption etc.