Is it possible to add new Team names
and use them for custom sides?
So instead of Republic - Mandalorians
and instead of CIS - Death Watch..
But without touching the vanilla team names!

I managed to in The Sith Wars, but you don't get icons. Here's how I did it:
In the unit loading, make it like this:
SetupTeams{
ABC = {
team = ABC,
units = 12,
reinforcements = -1,
soldier = { "civ_inf_fumasu",1,2},
assault = { "civ_inf_aphotic", 1,2},
engineer= { "civ_inf_saber", 1,2},
sniper = { "civ_inf_vader", 1,2},
officer = { "", 1,2},
special = { "", 1,2},
},
}

And later in the LUA, anytime it is looking for the team it was before (rep in your case), change it to your new name. example:
SetBleedingVoiceOver(ALL, ALL, "all_off_com_report_us_overwhelmed", 1)
SetBleedingVoiceOver(ALL, ABC, "all_off_com_report_enemy_losing", 1)
SetBleedingVoiceOver(ABC, ALL, "imp_off_com_report_enemy_losing", 1)
SetBleedingVoiceOver(ABC, ABC, "imp_off_com_report_us_overwhelmed", 1)

Then, when you go to your localize tool, you'll want to go to level, map you are changing, and add two keys (or rename if existing)
locals
local

And call them both what you want your team to be called.

Thanks, but both sides are now called jawa. I want the the cis renamed to Mandalorians, and Republic to death watch...
I renamed local and locals but it didn't work


Edit:
I've found a way to do this =)
I've just looked at the Hero-Assault scripts.
I've seen that I just need to paste "hero" as team name instead of rep, and simply
localize the "hero" side to Death Watch^^ Then I've just used KingPin's solution for the other side, and renamed the localisation "locals" to "Mandalorians",
It didn't work the first try cause I'm using the German SWBF2 Version and needed to localize it in the German section!
So, Thanks KingPin=)