To create a faction you must first choose a faction name from the list. Using the in-game chat bar, use the command, ~ffn (find faction names) and review the list. It is a long list, so you can press F2 to save it to a log file and review it there instead.
View a comprehensive list of faction names, both used and unused, here: 
You may request to have a new Faction name added to the list here: