I can see that for sure. Well, why not start from first principles? It would help to know a bit more about the Reclaimers and the earth/colonial military from which they are descended. Was it a unified military command or were there divisions between naval and infantry branches? Was there any particular cultural heritage evident in the military structure before the war with the X'Lanthos? For example, was the military arranged in unified combat regiments or in DIY combat theatre brigades? That is, was there a strong regimental tradition or were units detailed their roles in combat based on experience and spreadsheets in HQ, regardless of regimental origin?
The problem is that most designations for unit types/troop types fall into one of two categories - very basic technical descriptions like marine, seabee, or dragoon or hereditary regimental designations drawn from the regimental colors, the region of origin, or the place where they are traditionally stationed, like Green Berets or Borderers. The majority of the basic technical designations have been used quite often and the ones that haven't been are generally very culture specific. There are still some options. Fusilier is not very commonly used in games and has been used in a number of different contexts so it is one possibility but it does not quite feel right. It's a bit too antiquated for the very high-tech feel of the faction. Cavalry names like Hussars, Dragoons, and Lancers work a bit better but of them only Dragoons feel at all right since the Hussars and the Lancers were both exclusively mounted troops. Dragoons also have not been used very often in modern gaming so that's definitely a possibility.
It still, however, is not an extremely modern-sounding name. It's much less era-limiting than something like fusilier but I think given the context of the rest of the faction we can do a bit better. Given the context of strong, close ranged firepower, elite unit statistics, and low numbers, something very modern like "strike team" sounds like it would fit the bill well. It sounds like commando operations, special training, and a very violence-oriented mindset.
However, looking at the faction names - Warden, Guards, Aegis, Redeemer, and the faction name itself, Reclaimers - I'm getting quite a "holy war" feel from them as a whole. That leads me to consider a name like "crusaders." It, despite superficially being antiquated, is not really very limiting as far as image, it's not too frequently used in the context of modern gaming, and it does help accentuate that theme in the faction names. At the end of the day, though, I have to say, I just don't think we know enough to make more constructive suggestions on that front.