Did he trademark it? Did he sign that away when HBO did the TV series?
Not that it matters for a passport. But it’s entirely likely a media company owns the trademark for a book character rather than the author.
I think it would be more likely that grrm licensed the trademark and IP to HBO/Discovery rather than sell it. But I don’t actually know
https://trademarks.ipo.gov.uk/ipo-tmcase/page/Results/1/UK00917519208
HBO owns it in the UK. Weirdly, I couldn’t find an active entry in the US database.