War Dogs by Greg Bear uses the term Skyrines, a portmanteau of "sky" and "marine". If you don't like the use of the term "sky", you could substitute it for another term like say, "cosmo", to get "Cosmorine."
Other examples may include:
astroldier - combining Astro and Soldier. A bit hard on your tongues though, decreasing efficiency in a military setting.
Plasfo - PLanetary ASsault FOrce. This one is a bit more heavy on stereotypical military terminology, but gets the job done.
Look Into Linguistic Roots
The term "marine" is derived from French (French "marine", from Latin "marinus", derived from "mare"). We could do the same but with the term "space". In French, the term for space is "espace" according to Google Translate, so space marines could potentially be called "espatiers" (pronounced "espaciers" as in "spatial").
(I got the above example from http://www.projectrho.com/public_html/rocket/astromilitary.php#terminology)
But this isn't the 1800s and presumably not everyone speaks a Latin-derived language. So you could potentially play around with linguistics and lore to create your terminology. For instance, I could have a world where there is a second space race and China comes out on top, and have terminologies be based on Chinese.
But regardless of language, we need to consider what would be practical. In a military setting, communication needs to be short and precise, and easy to say, so we should decrease the number of syllables while keeping the meaning clear. If you want to stick to English and keep it linguistically reasonable, I say you should get common phrases like in the other answers and play around with them (see above section).