It's one TV licence per property or address (as far as I'm aware)
However, I wouldn't get a TV licence. It is only needed to watch programmes live or anything on the BBC. You can watch all itv, channel 4 etc. programmes on catch up without it.
Additionally, as long as your laptop (or device you are watching it on) isn't plugged in to a power source then you can still be classed as using your parent's TV licence. This is because it was considered ridiculous to get a licence when you were travelling away elsewhere in the UK and you can still watch stuff on tv then, so it's sort of seen as more of a travelling licence when you're on holiday (if that makes sense)