What Surname Are Salt Children Given?

[The Bard of Banefort]

Unlike bastards, salt children are considered legitimate offspring on the Iron Islands and can even inherit lands and titles if their sire has no living Ironborn children at the time of his death. Since they're not  considered illegitimate, I doubt salt children would bear the name 'Pyke,' but it's not clear if they are given their father's surname, either, since they do have a lower status than offspring from 'rock' marriages. As far as I can recall, we are never given an answer in the books. What are some of your ideas for how salt children are named on the Iron Islands? 

[Jaehaerys Tyrell]

I think they would receive the house name, and there’d be no official distinction except in terms of inheritance, where they’d come behind their rock-siblings.

[Tygett Lannister]

I would suggest adding Salty before family name, so if Theon had a salt child he would be called:

Salty-Greyjoy

that would express his birth status and emotions regarding succession.

[Corvo the Crow]

There was a house related to Greyjoys (or perhaps Hoares, can't recall) through children of Salt Wives. They were among the men Victarion left in MC.

[Universal Sword Donor]

3 hours ago, Corvo the Crow said:

There was a house related to Greyjoys (or perhaps Hoares, can't recall) through children of Salt Wives. They were among the men Victarion left in MC.

Codds and Humbles aren't mentioned as related to the Greyjoys (but are descended from salt wives), but we learn of distant cousins of the Asha who follow her.

[Corvo the Crow]

15 minutes ago, Universal Sword Donor said:

Codds and Humbles aren't mentioned as related to the Greyjoys (but are descended from salt wives), but we learn of distant cousins of the Asha who follow her.

My mistake then, but it gives us some idea on salt children.

[Universal Sword Donor]

28 minutes ago, Corvo the Crow said:

My mistake then, but it gives us some idea on salt children.

I always assumed they got the last name

[Jon Fossoway]

10 hours ago, Tygett Lannister said:

I would suggest adding Salty before family name, so if Theon had a salt child he would be called:

Salty-Greyjoy

that would express his birth status and emotions regarding succession.

Hahahaha good one 

[The Bard of Banefort]

It appears that we can deduce an answer based on Fire and Blood. Both of Dalton Greyjoy's salt sons - Toron and Rodrik - were put forward as claimants for the Seastone Chair, with no mention of them changing their names or being a poor choice due to not having Ironborn mothers. This makes me think that salt children are born with their father's surname. It makes sense, I suppose - if people can keep track of which trueborn son is older than the other, then they should be able to remember which ones come from a salt marriage.