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Starks: Live up north they're really honorable and loyal and they have pet wolves. Possible names: Sansa, Arya, Lyanna

Lannisters: Rich as hell, they rule the west and want to get rid of the current king. Possible names: Cersei, Joanna, Genna

Tyrells: They rule the Reach and have some pretty massive, awesome armies. They're pretty rich too. Possible names: Olenna, Margaery, Elinor

Martells: They rule the southernmost part of Westeros and are known for being beautiful and what not. Possible names: Elia, Arianne, Nymeria

Baraetheons: Rule the stormlands, pretty much just badasses. Possible names: Shireen, Bella, Barra

Targaryens: Current king is a Targaryen. They conquered Westeros like 2000 years ago. Possible names: Rhaenerya, Visenya, Daenerys

Arryn: They rule the Eyrie and are also pretty honorable. They push people to their deaths if found guilty of a crime. Possible name: Alys, Elys, Rowena

Tully: They rule over the Riverlands and are just pretty cool people. Really into family. Possible names: Catelyn, Lyssa, Minisa

Greyjoys: Rule the Iron Islands. Warriors. Possible names: Asha, Allanys

Those are some of the bigger houses. Once you pick a house I can help you find a picture