I don't know exact name, but it should be USB cable anyway (because it is that).
I doubt there is new one to buy (i don't think they produce them separately).
Anyways, you don't need to buy new one, you can repair current one without problem. All you need to do is to find out where the contact is lost, cut the cable there (usually it is just one wire if not contact on jack), remove that whole part maybe (few cm, inch etc.), reconnect, isolate and secure, mask it (for aesthetic reasons) and you are good to go.
All you need is way to measure resistance (every digital voltmeter can do it, just set it to Ohms), then, if cable is good, resistance is usually read as 0. You need isolator (type of tape for isolation), and maybe you can do sleeving for that part where you fixed it.
But, don't take my word, maybe there is actual cable to buy (i doubt).