SF theme

I have this mechanic, there are "rebels" that start a rebelion/coup/usurp and try to defeat you (the Emperor). They don't try to become independent or do it because they are unhappy (but that might be a factor too - people support them more if they are unhappy), they want to take over the power or simply destroy you.

I have a problem because the word "rebels" instantly gives you an impression of "poor honest people who fight the corrupted government", since that's the recurring theme nowadays :D While it's more like "a secret organization that brainwashed/coerced/terrorized part of population and now they started a rebellion".

I need, I don't know, a different name for this? Or some better explanation I could give to the player?

When we support a group, we call them opposition groups, militias, rebels... When we don't, they're (in order of hostility) separatists, insurgents, terrorists.

vernacular can arise from other criteria, eg. a group prominently employing a symbol (or other strong association), negating the need for handles that reference their alignment.

The leaders of a coup?

Couldn't it simply be "House of whatever" meets "Sons of the Harpy"? (a different house or a relative like uncle et al)

This group may simply try to overthrow Emperor to claim throne.