If you're in the official faction, then yes you should be using the official faction ID. Because as an official faction member, as mentioned above, you'll more than likely have added lines and less restrictions. Say you are doing something that an official faction is allowed but the indie is not, and you are tagged as official but have the indie ID. That could be confusing to people outside the faction that you encounter and they could submit a violation report on you due to that. Just creates a headache.
tl;dr - if you're in an official faction, and your ship is tagged official, get the official faction ID. If someone gives you crap for this, ask someone else in the faction, or ping an Admin so they can switch it for you.