What you do with your faction is totally up to you. If you would like to become an Ageira Technologies player faction, I will not stop you. However, as Summer said earlier, you cannot simply switch IDs: changes to your roleplay, even your faction's name, will be required to fit in properly.
Addendum:
If you are interested in Roleplaying a Liberty trade/shipping faction that is not Interspace Commerce, I would recommend Universal Shipping.
Other corporations with no player factions:
- Synth Foods
- Planetform
- Kruger Minerals