Unfortunately, what you're looking for are the Blades. But if that's not the flavor of your tea, you can "create" your own faction.
Assuming "secrecy" ... well, like U.S. Black Ops or the British SAS are so secret no one knows about them ...

... well, Knights would be out of the question because they are too public. This would be a group that everyone would "know" about but no one would "know anything" about. Like the KGB or parts of the CIA. They would be urban legend as much as anything. Maybe they exist; maybe they don't.
To be realistic, the name would have to have no meaning unless you knew what they were. Something like Men in Black ... (which always made me wonder what they called it when women joined) .... MiB ... the name means nothing.
In Cyrodill, they could be called the "Men in Fur." Whenever they killed someone, people would say, "Did you hear about Mankar Camoran ... he just got MiFfed!"
Allrighty, then.
Other suggestions: The Society. The Several (assuming a few ultra secret members that answered only to the Elder Council). Thinking medieval: Inquisitors, Tribunals, the Seydana (or Seydania) (ancient assassins). Another cool one would be "Ashinai-Risqu" (know or knowledge of duty - an ancient group of secret assassins). The Skulls. The Never-Born (because they give up their identities).
Are you giving your character a name or an eight digit identifying number?

~ Dani ~