Why Bran refused to answer? Well only Bran can tell but if we had to venture a guess I'd say that is because Bran has repeatedly told people that he doesn't really feel or need anything, he's mostly apathetic to whatever is happening around him. So as far as they can guess, Storm's End lacks a lord and so do the Stormlands as a whole. Nobody knows any other Baratheon, nor have they heard any news of a Stormlander resurgence after Stannis' demise.

Yet as it happened, the known Baratheons were all dead at that moment, the real and the feigned ones. Had she asked that after Stannis died (And Shireen had been alive), their answer would have been Shireen Baratheon (Or Lord Stannis' little girl for those who couldn't recall her name). Had she asked that question after Renly died, their answer would have been Stannis Baratheon. Had Daenerys asked that Question after Robert died, they'd have all answered Renly Baratheon. Nobles grow up learning about other noble families' family trees, particularly their neighbours and great Houses. Well that is because there was no Lord of Storm's End as far as they knew or we know.

Game of thrones storms end