From the original article [1]:

"That's not necessarily a problem. Netflix can produce a television series without confusing consumers, just as the military can train fighting astronauts without anyone mistakenly thinking the streamer is sponsoring such an academy.

Conflict potentially arises when trademark users begin trafficking in similar products. Imagine for a moment that a “Space Force” jumper begins appearing in retail stores. Who’s selling? The U.S. military or Netflix? Trademarks help clarify the source of goods and services."

So the US could also call it something like 'National Space Force' and the problem is solved.

[1] https://www.hollywoodreporter.com/thr-esq/trumps-space-force...