Yeah, "closed captioning", unfortunately, is pretty much the definitive term for that in the US. (Technically, I think it would be called EIA-608, but no one would know what I was talking about if I called it that.) It's encoded on a line in the blanking interval of the NTSC video. ATSC has a backwards-compatible version of it. But my understanding is that HDMI basically doesn't transmit data in a way that allows for a blanking interval.