I suggest "Spacor" for the general term along the lines of "Sailor" or "Soldier."
You also have "aviator" as a pattern reinforcer. "Airman" is problematic enough in this day and age for the base term. Besides, "Spaceman" sounds too alien. And "Spacine" to follow the Marines seems too ... off.
So Spacor it should be.
For ranks I suggest we follow the Air Force pattern. Space Force is within the Department of the Air Force, after all.
Officer ranks would stay the same but for the enlisted, from E-1 to E-9 we'd have Spacor Basic; Spacor; Spacor First Class; Senior Spacor; Staff Spacor; Technical Spacor; Master Spacor; Senior Master Spacor; and Chief Master Spacor, Command Chief Master Spacor, and Command Chief Master Spacor.
When we move outside the Earth-Moon system for a true Space Navy we can follow Navy practice--including their SEALs for a "ground" component. I had thoughts on that in that post:
I eagerly await the Space Force contribution to Special Operations Command, as I speculated over a decade ago:
A squad of [space-delivered] Marines would be a drop in the bucket on Earth, but in space in 20 years, 13 Marines would be a decisive ground force capable of entering and capturing anything any nation would put into orbit in this time frame.
Although obviously the term "marine" is not appropriate given the organizational structure. Special Space Service (SSS, or Triple S)? That would be homage to the British with their SAS and SBS.
Or mimic the SEALs with STARs--Space Tactical Assault Response. Or even better, Space Tactical Assault and Rescue. That opens up a Coast Guard type rescue mission in addition to a military role in space.
One day, there will be a story of STAR Team 6 exploits. But my clever names never get picked up.
A small special forces ground component is necessary for Space Force. If you want to go after a space station, orbiting satellites for close work, the Moon, or even Earth very rapidly from space. Call them Space, Moon, Orbital, Down teams: SMOD.
Okay, I'm not (totally) serious about SMOD. I'd stick with STAR for Space Force special forces and SSS for a future Space Navy ground force.
So there you go.
UPDATE: Wait, Space Marines Orbital Detachment! I'm feeling more comfortable with SMOD.
UPDATE: Sure, a Space Force ground-based offensive satellite jamming system is great, but I won't be satisfied until we can board and capture orbiting manned stations.