A TV show that likely won't be talked about by the time your kid is old enough to discuss it wouldn't bother me AT ALL. My middle name is after a TV character, so my mum says, I've never heard of the show, watched it or heard anyone else mention it.
This is a bit different, I think, as A Song of Ice and Fire is one of the top selling fantasy series of all time, which will likely not be forgotten as easily as a TV show and will probably find its way into future generations as a classic (though mature) read. As I mentioned I don't think most kids on the playground would be familiar with it as its content is quite inappropriate for young kids, but the lines blur a bit around high school age perhaps.