NPC Corps and Factions are different things Agent. You do work for an NPC Corp (for example Federation Navy) and you'll get a standings increase with them and the Faction (for example Gallente Federation).
Now, each NCP Corp has a few agents in it, this is probably what you're looking at to find who's available. Depending on the NCP Corp will depend which Faction it belongs to, but underneath their name on the info page will be a link to the Faction. Click on that link and you will be able to see how many other NPC Corps are part of that Faction. All those NPC Corps will have different agents exclusive to them and you may find many more who you can work for.
If you're stuck trying to find a decent agent near you, trying using
EVE Agents - EVE-Online Agent finder. Put in your Region, the Faction that you've been working for so far (not NPC Corp) and choose level 1, this will list all the agents in your Region linked to the Faction you've been working for so far. To find one you can use, look at the Required standing, most NPC Corps you will have a standing of 0.0 with them if you haven't worked for them before, killed their agents for other Factions and have no skills affecting standings, so find one close by and go work for him/her. Their quality generally relates to the rewards and standing increase you get for completing their missions, so the higher the better.
If cars had followed the same developmental path as computers, a Rolls Royce would cost £60, get a million miles per gallon and explode once a year, killing everyone inside.