List @@ # & /@ EdgeList[gFriendShip, "Rose" \[UndirectedEdge] _]
returns
{{"Anna", "Rose"}, {"Ben", "Rose"}, {"Rose", "Nora"}}
Another perhaps more transparent pattern matching approch might be,
EdgeList[gFriendShip,
"Rose" \[UndirectedEdge] _] /. {x_ \[UndirectedEdge] y_ :> {x, y}}
This is a 3 element list (rather than the 1 element list you suggested) because the
EdgeList returns a 3 element list. If you only wanted cases where only
{"Rose", "Nora"} is returned then you might use
Select or
Cases to get what you wish from the list above.