Ever since reading the ship section in the corebook, I've fancied the idea of having distinct factions, likely represented with named NPCs, aboard the ship that the PCs will have to interact with. It gives the ship more life (aside from the generated quirks), provides people for the PCs to consult to during deep-space voyages, and also has potential for creating interesting scenarios or even outright conflict when one particular group onboard doesn't quite see things eye-to-eye with the PCs.
Rather than having these "social" factions differentiated by upbringing as you're suggesting, though, I think the better division would be by profession aboard the ship. It's like making the "key parts of the ship" you mentioned at the end the actual factions, not just territory. One good reason to have it this is way is because your social factions are likely not going to be very stable in size or what they control as they are killed off during ship combat and replaced at port. Additionally, since the PCs are suppose to be the head-hanchos of the ship, chances are each would be highly influential with a particular faction, depending on their career.
These are some major factions I had in mind:
Filled with the most professional members of the crew, the bridge is likely the loyalest faction to the PCs, especially the Rogue Trader himself.
Consisting of those who man the main armaments of the ship. For a good reference on what their life is like, try reading the short story "Ancient History" in the Dark Imperium anthology.
For those who labor in the dirtiest, most dangerous parts of the ship, particularly the plasma drive. warp engine, void shield generator, and life-sustainer. Being stuck with the hardest work on a regular basis, I imagine that these guys will likely be the first to mutiny.
Distinct enough from the rest of engineering, this faction represents the emissaries sent by the Adeptus Mechanicus to perform the duties that only tech-priests could. Being especially secretive, however, they prefer to be left alone in their sanctum unless there are machines in need of aid. They also tend to frown upon actions that would strain the ship and forcefully involve themselves in any mission that involves recovering unusual technology, usually either by declaring it as blasphemous and therefore must undergo immediate destruction, or by demanding that the PCs hand over the tech to the Mechanicum for "further study". Naturally, the Explorator is well-connected with them.
Preachers and priests sent by the Ministorum to maintain moral and faith to the Imperial Creed aboard the ship. Their presence is even more apparent if a Temple Supplemental Component is on the ship. Relations with them may turn sour if the PCs end up dabbling in heretical activity a bit too often. The Missionary is obviously associated with them.
Often the best thing to actual soldiers, security is charged with maintaining order aboard the ship, as well as carrying out or defending against boarding actions. On occassion, the PCs may also be compelled to use them on expeditions to a planet's surface. The Arch-Militant easily fits into a commanding position among them.
The department of scribes and adepts who do all the record-keeping for the Rogue Trader's dynasty. They are greatly complimented by the Librarium Vault Supplemental Component. The Seneschal would know how to deal with them.
Although they are very, very few in number, the Navigators aboard the ship are alien enough from everyone else to warrant themselves as a faction. Additionally, they are backed by a very powerful organization, the Navis Nobilite, and demand a lot of respect for it. It is likely that they'll have a superiority complex over everyone "ungifted". This faction's prominence, however, is greatly diminished if one of the PCs is already a Navigator.