How could they be completely unrelated though, they were all made in the same group, of which there were about 33 but there was never another group of spartan IIs the next batch wasn't made in time and must have been killed on Reach. So all that leaves are the spartan Is with no armour, and then the secret spartan IIIs. Although just because they went by the call sign Omega team does not mean they are completely unrelated, in times that were needed the team with mix as to who has the needed skills in a situation. Like at Cote de Azur where John took linda and james with him and kelly and fred even though they were from different teams. The color teams even changed during the battle of Reach, I'm just guessing that blue is master chiefs favorite color. So because this is a different situation and they are most likely away form the rest of the spartans then another name might just be easier.
Alright boys we're going to run up this mountain and pee off the other side laughing!
We work as a team, we fight like warriors, and we will die brothers.