1) The current factions are like- in a different universe from each other, meaning they are not related and have their own stories. Tho, there are still some factions that have connections or are in the same story line wherein inter-galactic travel is possible via warp gates/jump gates or hyper-drives (powerful than the FTL). For example, the Voidians, NanoTrasens, Greenfire Industries, and Armament Intergalactica. ~Naming the galaxies would be difficult but possible, all we have to do is make our own universe just ONE> let the faction makers discuss, create and agree upon their territorial disputes and political connections, name their galaxies and connect their story lines> Create a discussion where every single galaxy that is controlled by a faction is listed> create a single major story line (consistent war for universal superiority) and multiple story lines where there are only some factions that are involved (inter-galactic war).
2) There are still some undiscovered parts which are yet to be conquered.
3) it would be easier to sort everything if all factions were in a single galaxy, but it would be more dynamic if it's in a single universe.
4) I have a faction called Universal Terran Armada, basically the faction of humans. Earth is their capital, they were rich and respected. Until an unknown threat just suddenly appeared and destroyed Earth.
If you want our factions to be more organized, you'll have to talk to all the faction makers.