That's an interesting idea, especially due to the fact that I have done exactly the same (with the Basilikon Agema model as well) What I did was to add them to the roster, edit their AoR and tweak their stats to match those of the Cohortes (sp?) Reformata. The rationale was that the Basileion (later Arche) would adapt to Roman tactics and create their own 'legionary' corps. So I named them Koorteis Makedonikai, or Makedonian Reformed Cohorts.

As for your case now, you could do the same as me, or you could name them Machairophoroi, asd you suggested. Actually, due to the fact that they wield Kopeis (plural), Kopidophoroi would be more correct. So Thorakitai Machairophoroi or Kopidophoroi

Regarding governments now, there are tons of names you could give them. It depends on the style you want to give them. For example, if you follow the Seleukid way of governship, you could name them Satrapeiai Makedonikai Stratiotikai, or Makedonian Military Satrapies. If you want something else, more like the Patris Makedonike but more Panhellenic (like I believe is your case), you should consider something like Patris Hellenike Makedonon (Hellenic Homeland of the Makedonians).

Hope this helped,
Maion