How do we know if a noble House of Westeros exists?

Question

There are seven houses listed in The Citadel which have no corresponding entry on A Wiki of Ice and Fire. These are:

• Cups
• Farrow
• Hawthorne
• Leek
• Penny
• Sawyer
• Suggs

I'm not sure whether these should be considered houses. None of the seven articles in the Citadel list words nor arms for any of these. There are two characters who appear to have the name "Penny" - Jon Penny and Ser Corliss Penny, and the former an orphan. There is one Farrow (Ser Richard Farrow,) one Leek (Ser Rufus,) one Suggs (Ser Clayton,) one Sawyer (Harry Sawyer,) and no Hawthornes. So the only thing pointing to the existence of any of these Houses are no more than two characters using it as a last name; and House Hawthorne appears to have a coat of arms, according to the Citadel.

The question is, when is a House a House? When there is a Lord? When they have a coat of arms? When they have a motto? Does the mere existence of these six characters imply that a House bearing that name must exist, or is it more complex? In another question, a user mentioned that only members of a noble house have last names, so I'm assuming that the existence of someone bearing a last name implies the existence of the House, but I'm not sure if this logic is sound.

Answer 1

From appearances in the books, Houses need not have any living members to still be remembered as a house. Once the house is set up, by either the king or a high lord, all of the family will be part of that house; whether they got land to begin with or lose the land somewhere in time, they will still be a house. So these houses you have listed are most likely minor houses, or great houses that have been replaced. They may or may not still have land somewhere in Westeros, and they may have multiple people left in their families, or they could be the last of their respective houses.