I'll let you off with the names, there's so darn many of them.
Here's a list of important people so far.
Starks:
Eddard "Ned": father
Catelyn "Cat": mother (nee Tully)
Robb: eldest son (wolf: Greywind)
Sansa: Eldest daughter (wolf: Lady)
Brandon "Bran": middle son (wolf: Summer)
Rickon : youngest son (wolf: Shaggydog)
Arya: youngest daughter (wolf: Nymeria)
Jon Snow: Ned's bastard (wolf: Ghost)
Theon Greyjoy: Ned's ward/hostage/prat
Bathareons
Robert: King dude
Renly: youngest brother (there's another brother, he's not around yet)
Cersei: Queen
Jaime Lannister: Cersei's twin brother.
Tyrion Lannister: the twins' younger brother; dwarf
Joffery: entitled little brat of a future king. (his siblings Myrcella and Tommen are lovely though.)
Council
Petyr "Littlefinger" Baelish: pimp
Grand Maester Pycelle: "doddery" old maester
Varys: Eunuch, spy master general
Targeryan
Danearys "Dany": exiled princess
Vysaris: Dany's elder brother
Khal Drogo: Dany's husband; tribal leader
Ser Jorah Mormont: exiled knight
Not sure who is at the Wall as of yet...
Lord Commander Mormont: big boss man; Jorah's dad
Ser Alister Thorne: master of arms, not very nice
Maester Aemon: nice guy, blind, could've been king
I think Pyp, Grenn and Dareon are there, not sure about Samwell Tarly and Dolorous Edd Tollett... you'll know them when you see them. There are those who would suggest 4 of those 5 aren't important enough to mention, but Dolorous Edd is a favourite of mine.
Anyone I've forgotten, let me know... trying not to be spoilery.
Glad you are enjoying it.