Feedback on guild names

For playtesting purposes, those names you have selected are fine. For narrative/thematic purposes, they are not so effective.

For example, is there a name of a Royal Family you could use for the Crown Faction? Some examples:
The Boldran Empire
The Kindom of Festonia
Republic of Kathoom

Do the outlaws have a leader from whom they could take their name? Maybe a specific tactic or tool/weapon?
The Crescent Blades
Tarak's Reavers
The Night-Singers

Can the forest dwellers take their name from their enchanted forest, and/or a dominating feature of their wilderness domain?
Emerald Wardens
The Harvesters
Knollwood Denizens

There are lots of different directions you can go with this, but I recommend you find a way to link them to the game world to add immersion and cement the theme.

Way t' be, Let, you've got some great names there. Personally (and seriously, this is soooo subjective) I prefer names like the "Emerald Wardens" to names like "Republic of Kathoom".

Kathoom isn't so bad, but many RPG style games have names like "Brithoniel" and "Forstoria" and I can't remember the damn things for the life of me. I think descriptive names are more functional than the RPG-name-generator variety, in my experience.

I also have no problem with the straight-shot approach you've taken with "The Crown" "Forest Dwellers" and "Outlaws." Names like these fly under the radar; you don't love 'em, you don't hate 'em, but you recognize what they represent immediately and move on with no thought about it at all.

I took this approach with my kids -- no fancy spellings, no names from a book that nobody's read. Straight up names that sound nice, but you know 'em when you hear 'em and you know how to spell them without asking. hahaha

So it depends on how important story immersion is; that's the big factor. If you want people to fall in love with your world, Let has you covered with the right idea. But if it's just a matter of "here's a fantasy world -- go play" then what you've got is fine, imho.